I have always assumed that- since the Gift has no direct effect on Intelligence (or indeed any other characteristic) the general distribution of particular Characteristics among children with the Gift was similar to the distribution of those values among the general population. Furthermore, I can see no means by which the Intelligence of a child with the Gift would affect their odds of being discovered by a Hermetic magus/a.
However, few magi (and still fewer player characters) would choose to train an apprentice with negative (or even zero) Int. So what happens to all the Gifted kids that aren't worth anyone's time to train? Does House Tremere buy them and assign someone to train them? Do Tytali challenge each other to turn the dumbest possible kid into a respectable magus? Or do they just get left alone to live their (probably miserable, given the social effects of the Gift) lives with whatever supernatural ability they end up learning naturally?
There are more groups than just the Order which is based around individuals with the Gift. Not all of them are scholarly groups in which Intelligence is the most valuable Characteristic.
The Order has a total membership which is roughly equal to 20% of the Gifted Population of Europe. That percentage does not include the Gifted population of the border Tribunals, which could drop the Orders percentage to less than 10% of the Gifted in their areas. Even without gaining new Apprentices from border and outside areas, you still have 80% of the Gifted population who are not members.
While some portion of them end up spending their "miserable lives alone with whatever supernatural ability they end up learning naturally", a portion (if not most of them) end up being adopted into a Hedge Tradition. There is a high enough demand for Gifted individuals that many Hedge Traditions have developed the ability to teach some measure of their abilities to those without the Gift.
Ah, perhaps I wasn't clear enough. What happens to the low-Int Gifted children, who are found by a Hermetic magus searching for an apprentice? Do they just get written off as not worth training, or is there enough demand for Gifted children of any stripe even within the Order for a magus in possession of a gifted brat he doesn't want to train to find a buyer?
Obviously the proportion of gifted kids found by Hermetic magi is rather small, because Hermetic magi just don't spend that much time in mundane population centers, and equally obviously a lot of the remainder are going to end up in some hedge tradition or other, but I was more curious about the reaction of your typical Hermetic magus in search of an apprentice to a Gifted candidate that he doesn't really want to burden himself with. Ignore them? Sell them to an Ex Misc or otherwise-poorly-regarded magus for a few pawns of vis? Sell them to the fae for favors or vis? Sell them to a Tremere-Academy-of-Pumping-Out-Gauntleted-Magi-To-Inflate-Our-Elders-Proxy-Voting-Sigil-Count? Or just pass on word to the Redcaps to inform whoever they please, just in case someone's interested?
Part of that depends on the individual Saga. In some, the Magi (and Order in general) are extremely picky. In others they train every Gifted child they find. On average the ones I have been part of tend to slant towards being picky, with Gifted children who are not "desirable" being passed over or given/sold to others.
In one of the books, I could not find it, I remember them mentioning that the gift and above average intelligence are correlated. Obviously merely a narrative conceit to explain this. Though there is the low Int Crimon at Jardin in Through the Aegis.
Not to mention there are probably plenty of Flambeau willing to teach a gifted child who is a bruiser but not very intelligent.
Another question worth asking is, in the ars magica universe how much if ones intelligence is predetermined from birth and how is determined by the environment, such as rigorous training imposed by a magus who values intelligence?
Most of it is set at birth.
Base stats of a character are determined at birth.
Virtues and flaws like "Improved Characteristics" or "Weak characteristics" are also typically obtained from birth, but can be obtained later as well.
I think that the general body of magi within the order is more than willing to accept apprentices with non-negative intelligence.
Sure some lab rats and other academic types might say no to any that dont have 3+ scores in Intelligence. But for most magi less can probably do. It is worth mentioning that for actually doing magic in practice positive scores in Stamina and to a lesser extent Perception and Quickness are also very important. Stamina because it adds to casting scores. Perception because it is used in craft magic and to determine what is going on and Quickness for its value in winning fights, since many fights are likely to have their outcome determined by who goes first.
These traits are likely to be more valued by magi focusing on either the practical side of casting spells, or the application of magic in combat.
Political magi will likely value high scores in Presence and Communication just as much as Intelligence.
Player characters will tend to want special apprentices and as such will be more picky than a reasonable magus within the setting.
Perhaps this text helps with the initial question (HoH:S p.55 Less Intelligent Magi?):
Sagas vary concerning the prevalence of The Gift. In sagas where The Gift is rare, and mundane hostility to magi is acute, House Jerbiton’s magi may select apprentices with serious Flaws, provided they have the Gentle Gift. As an example, the usual Intelligence score for magi described in earlier supplements is +3. An Intelligence score less than +3 reflects a premium placed upon Gentle Giftedness by masters in House Jerbiton. As a counterbalance, these apprentices are often healthier and more charismatic than their sodales from other Houses.
In particular the text shows, how the description of typical apprentices in ArM5 p.106, templates of beginning magi in ArM5 p.24ff and early examples like "Semita Errabunda" covenant can relate to the general population of Gifted children in different sagas.
While you are right about PCs, I doubt that the general statement is true, as has been pointed out. Intelligence really is not that important, except in the role as lab assistant, for the parens. Even for learning spells, low Int can be compensated with lab improvements and reading up on arts and magic theory, and with a good library of lab texts, it is not going to matter so much.
The list of possible answers is long.
Some magi take an apprentice for company, and do not care whether they become masters of their arts.
Some magi invest in rituals to increase the apprentice's Int.
Maybe Intelligence and Gift are correlated.
Maybe low-Int Gifted individuals have such a short life expectancy that they are under-represented.
Some magi want to train apprentices with other abilities, and may therefore discount Intelligence.
For Jerbiton, this is canon. They prioritise Gentle Gift.
Tremere is likely, if they need the numbers, to take low-Int apprentices and steer them into a combat branch.
Some lineages may depend on particular personalities more than characteristics. Criamon springs to mind, but this may be true also for Merinita and Bjornar.
If there is a shortage of apprentices, everybody but the lab rats, is likely to take what they get. A low-Int magus can still be good in many things.
Intelligence is not that easy to gauge, so quite likely some low-Int apprentices have their arts opened before the parens realises. Some of them may be trained fully out of a sense of obligation. Some may be abandoned, and never picked up by another parens. Some of them may actually be allowed to self-study and eventually gauntlet.
Probably influenced by the fact that gifted children can be rejected or abandoned or worse by their Gift's social penalty, and that children with low int (and also low sta, which is also commonly high in many magi) probably tend to have a lower survival rate in these conditions.
In other words I'd say they tend to be smart because the not-so-smart die before they are found.
That being said we'd been slowly pulling down the Int average from magi from 3 to 2, mostly because I'd like to see some variety there. It took time but now any value from 1 to 3 is quite common. I'd used some NPC magi with 0 or -1 values there going not that bad.
To summarize what many have stated: canonically (and this was true in previous editions as well) Gifted children tend to have high Int; this means that most of the time, when a magus looks for someone Gifted as an apprentice, he'll get a high Int apprentice with no extra effort.
Now, what about the dumb ones? As has been pointed out, there are many, many niche areas where low Int can be forgiven in exchange for some other quality that some master may want in their student (and if that's some other magus, a trade can often be arranged). Let me list just a few.
The Gentle Gift. Important in magi who want to interact with mundanes (obviously Jerbitons, but there are many other possibilities, from a specialized Tremere vexillation to Pralicians interacting with hedge wizards).
Blood kinship, either with the magus, others of his House (crucial for Mercere, who will train their own no matter what), or perhaps some figure of great importance, political or mystical.
Great ability in communication. Important in "political" magi, but also crucial for those interested in teaching. In our saga, an Incomprehensible, very low Com Bonisagus specifically sought out an apprentice with Good Teacher so that he could ... ahem ...edit the master's work to make it more accessible (put less kindly: so that the master could distribute the apprentice's Tractatus as if they were the master's very own).
Fullfilment of a bargain. Sometimes you promise someone to train a specific apprentice as part of a bargain -- implicit or explicit: maybe there's a Geas on you to never refuse training an apprentice if you do not already have one, and placing a similar Geas on them is part of your Tradition.
Destiny. Sometimes you just know you are supposed to train a certain child, no matter how unsuited the child looks (typical for many Criamons).
A rare quality of mystical significance. Perhaps the master hopes to integrate that quality into Hermetic Magic (several Bonisagus magi would fit the bill, but also Pralicians). Perhaps it's indispensable for training in the Tradition: e.g. True Faith or Leprosy (indispensable for Tytalus Leper magi, and apparently "new generation ones" no longer inherit it from their masters).
The right temperament. Many Flambeau will prize that even in a low Intelligence individual -- as someone once stated, "any sufficiently brave person is indistinguishable from a fool". Tremere, too, would rather take an apprentice with just average Intelligence, but the right "team player" attitude, rather a smart but highly individualistic one. In fact, I think the House that will prize temperament the most is House Guernicus.
A sufficienly pitiful existance as a mundane. People take in stray dogs all the time!
I had so much fun playing for a few sessions a Quaesitor with -5 Intelligence, but the Virtues Charmed Life (which incorporates Luck), Premonitions, Intuition, and a version of "Supernatural Beauty" (HoH:S) tied not to beauty but to stupidity ("Supernatural Fool"). In the end, always right, but always for the wrong reasons
The in play range I have seen averages to ~2 going back to 3rd Edition. Normally only Bonisagus or the very scholarly focused end up with 3+, while many of the Houses who focus in other areas have ended up at 1. I have only seen a couple with 0 and none that I can remember with a negative. Those numbers are specifically for PCs.
One thing I have noticed is that "Casting Specialist" of all types (Combat, Spont, Ritual to a lesser extent) tend to focus as much if not more on Stamina than Intelligence. The same for "Finesse Casters" (Creo & Rego) and Perception. For a Combat Magus, high Intelligence just is not as valuable as Stamina. Even Perception and Quickness can prove more valuable to them depending on their spell types and fighting style.
Overall observations have been Int and/or Sta are common across the board, with Qik, Per, and Com getting focus when they meet the character concept. Str, Dex, and Pre tend to end up as dump stats the most often. One of my fav characters was a 3rd Edition Jerbiton with Int 1, Per 0, Str -2, Sta 3, Pre 2, Com 2, Dex -1, Qik -1. The Gentle Gift was cheap back then (only 1 Virtue point).