I do not think the implication above is that The Gift was initiated... I think it's assumed that the founders all already had the gift. Hedge Magic goes into some detail about other traditions that have Gifted members.
I believe the intent was that Bonisagus made an initiation script that effectively reshaped one's gift as the Hermetic version. You could treat this as a weird sort of Ordeal, where they lose the gift to gain the gift.
While all that is reasonable, that still leaves the issue of what happened to Ordo Miscellenea's hedge wizards, i.e. most of them, mostly likely all without the Gift.
Either the hedge wizards of Order Miscellenea were allowed to train apprentices and then admit them into the Order of Hermes, as well as admit new hedge wizards into their House, which would mean the Hermetic tradition would have been rapidly outnumbered by voting hedge wizards, or they weren't allowed to train and admit apprentices, or recruit entirely new members, into the Order of Hermes, which I do not see them accepting in the first place upon receiving Trianoma's offer or that they would accept it sitting down if it became a de facto truth later on.
Do we know that Pralix took non-Gifted magicians into ExMisc? You're probably more up on the recent source material here than me.
My view is that the foundation of ExMisc changed the OOH from an organization of Hermetic wizards to a broader organization of Gifted magicians. I don't believe the non-Gifted ever made up a substantial component of the Order, except for the Mercere and other particularly useful individuals.
Do recall, IRL, the concept of UnGifted hedge wizards with arts was introduced long after the concept of the Ordo Miscellenea, so I think no real effort has been made to explain why a character idea that didn't exist yet was unaccounted for. 
More practically, IIRC Pralix recruited hedge wizards in part by teaching them Parma Magica. Since you need to be Gifted to learn Parma, logically everyone Pralix recruited was a Gifted hedge wizard.
I would say that they are considered to be members of their traditions, but not Hermetic magi unless they are invited to join because they are so powerful as to play even with Philippus Niger. They will still be required to more or less respect the Code, but since they are not protected by it, they are fair game for retailation by OoH members if they start messing around too much with mundanes, the fay et al.
They will certainly NOT have Parma Magica. Any of them that displays general MR will be killed first, questioned via InMe later.
In other words, exMisc is for Gifted individuals. The army of pralix would include quirte a few of those, and A LOT of people that were not granted membership in the OoH when exMisc was formed. Not that 99% of them would care much about it. it was that settlement or war of annihilation. remember that the OoH was small at the time. they would have won, but the cost would have been extremely high to the nascent order, maybe even a deadly blow.
Xavi
No, we don't (or at least I don't).
I find it strains credulity to state that any particular population of hedge wizards is all, or mostly-all, Gifted.
When Pralix established Ordo Miscellenea, it was specifically recruiting from among those that the Order of Hermes had already passed over:
It took almost a year before Trianoma showed up to Pralix with her deal to join the Order of Hermes. Ordo Miscellenea, in one year, recruited enough hedge wizards so that when they became Ex Miscellenea, their addition doubled the size of the Order of Hermes.
The Order of Hermes had already been combing Europe for some fifty years or more for Gifted members, and Gifted apprentice searches had probably been underway for a decade or two, and still Ex Miscellenea had enough members to double the Order's size. I just find it hard to believe that even a majority of them were Gifted. The fluff seems to go out of its way to paint them as hedge wizards, of the sort that would not normally be asked to join the Order. Specifically, that they weren't Gifted.
I haven't found a reference to that. Can you point me at that information?
A Gifted folk witch would not be asked to join the Order of Hermes (except in special circumstances).
A Gifted folk witch would be asked to join the Ordo Miscellanea.
Being Gifted and deserving "normal" membership in the eyes of the elitist OoH are 2 different things. IMO at least 
That fits pretty well with the idea that the OOH was originally made up only of practitioners of Hermetic Magic (i.e., the 15 Arts). Only so many apprentices can be trained in fifty years using the one at a time system traditional to the Order, so I don't expect they would be anywhere close to running through the Gifted population of Europe. If you think of Hermetic Magic as being an exclusively Roman (or at least Mediterranean) thing, consider all of the populations of Northern or Eastern origin that must practice other "hedgier" magics. The real question is maybe why none of these magics survived within the OOH; the answer probably being the elitisim of the Hermetics.
Good point. And I'm still not sure I like the idea of whole traditions of UnGifted magicians. I think I prefer the old paradigm, where you had Gifted Hermetics, Gifted practitioners of other traditons, like the Picts, and UnGifted hedge magicians with one or two supernatural abilities. Allowing anyone to use complex magics muddies the waters.
Do you have the old 2nd edition sourcebooks?
Again, you've got to remember that IRL this background long pre-dates the current edition and it's rules and assumptions. There are inconsistancies. I still remember the days when the Tremere were turning into vampires.
I don't agree with your supposition. Do we have a RAW basis for assuming that most or all did not have the gift? I feel like the RAW references I've seen have suggested that the gift has become harder to find with the proliferation of dominion auras, leading me to think that, in the time of the founders, people with the gift were more common. Without knowing more about that particular tradition, I'm not sure I can guess whether it was one that required the gift or not.
Keep in mind that, according to RAW, Ex Miscellanea outnumbers the rest of the Houses combined, and this hasn't led to an Ex Miscellanea rise to political power, because the nature of the group is that it isn't as cohesive as the other Houses. It's quite possible that the Ordo Miscellenea had a similar problem, especially if, when they were brought in, they were divided among the Societates.
I've been picking up Ars Magica since 1991. I have the ArM2 and tOoH. I did not find Covenants at the time.
Yesterday I was reading through Lion of the North, and it says straight out that many of Pralix's allies had learned Parma Magica, even if they were inexperienced by their first battle.
Hmmm. I'll have to think about it further.
That was when White Wolf was trying to fit Ars Magica's Mythic Europe into the history of the World of Darkness. I still remember having several Ars Magica versus World of Darkness discussions with friends in the mid 1990s regarding House Tremere (from ArM), Clan Tremere (from Vampire), and further fluff from Mage regarding it all. I never really held too closely with all that in regard to Ars Magica.
While House Tremere may have now been disconnected with the idea of Tremere slaying Salubri to become a high-generation vampire, which I'm okay with, they're still in the Transylvania area, and well, I'm sure there are a few vampires running around out there, and House Tremere is a tradition descendant from necromancers (at least it is in ArM5). </evil laughter>
Let's approach my personal concern about hedge wizards and the Gift from the reverse angle.
Hypothetical Given: All hedge wizards have the Gift, and if they desire, can learn Hermetic Magic. Therefore, everyone queried by Trianoma, the other Founders (including the group of hedge wizards that joined the Order of Hermes en masse when Flambeau killed their leader), all of Pralix's allies during the war against Dav'nalleous, recruits into Ordo Miscellenea, all later additions to Ex Miscellenea, and all the rest, can all learn Hermetic Magic, including Parma Magica.
Does anyone see any issues with this?
We need to break this down to discuss it from the prespective of the AM5 rules, as opposed to the setting alone.
I'm cool with getting rid of the ungifted hedgies from Hedge Magic Revised. The traditions in that book work best for the Gifted.
Here's a rules issue. According to AM5, the Gifted only get to express their Gift according to one system of magic. Hermetic Magi can't just pick up Pictish or Witch magics, because their gift has already been expressed with the opening of the Hermetic Arts. The same works in reverse for Hedge Magicians who would like to learn Hermetic Magic. It's possible to open the Hermetic Arts for a hedge wizard, but it's very difficult and effectively damn near impossible for an advanced hedge wizard. See AM5 page 107 or Societates pg. 128.
The nature of the breakthrough that created Parma makes that ability universal, rather than specifically Hermetic. Therefore all Gifted people can learn it, regardless of whether their Arts are open. So no problems with this one.
This is incorrect. The rules you cite do not bar opening of the Gift in either direction if it has already been opened. According to HMRE the sections you cite "do not address the possibility of the apprentice's Gift being already Opened by another tradition." HMRE gives specifics on how to Open the Gift a second time, and it can be done even if you have your Hermetic Arts Opened first (stated explicitly). The rules are on pages 7 and 8, the particulars being on the lower-left of page 8.
Chris
Interesting. I wasn't familiar with the rules on 7-8 of HMRE. I'd have to think more about how hard that makes it to open non-Hermetic magic for a Hermetic.
With regard to the issue RainOfSteel raised, opening the Hermetic Arts of a Hedgie, pg. 8 of HMRE actually makes it harder than before, by adding 30 to the InVi lab total required. I see nothing that eliminates the requirements from AM5 or Societates. So to open the Hermetic Arts of a Gruagach with Give and Take would require an extra lab total of 30 (for having opened Gruagach Magic), plus minimum 30 for Give (higher if his Give score is above 6), plus minumum 30 and perhaps more for Take. As I say, good luck in practice opening the Arts of an experienced Hedgie. Which is as it should be, IMO.
Isn't Rival magic who explains that the first tradition opening and all who was learned is now lost when the gift is reopened?
Hedge Magic Revised and Rival Magic are sitting in a shopping cart, waiting for me to order them. As soon as the budget permits, I'll get them.
Well, with the expection of those hedge wizards whose powers are limited to Supernatural Abilities, I understand this to have been the opperating assumption until fairly recently. It wasn't until the release of Hedge Magic that the idea of UnGift wizards really established itself in Ars Magica canon... though the idea of magicians with a "weak" or "partial" Gift is long standing IIRC.
I'd recommend you pick one of the two and see if that gives you enough non-Hermetic traditions. Both books have interesting material in them but the rules overload from using all of the traditions in the two is enough to make your head explode. One of the reasons I advocate non-OOH hermetics is just so you can use a common rules set for them.