Yep. The Gift represents the ability to (in theory) conventionally learn (ie, by being taught it or reading it out of a book) any magic system that is learnable. As such, one of the way you can figure out if someone has the Gift (aside from them being really creepy) is if they start accidentally learning magical techniques by osmosis.
However, the restriction is that the more you learn, the more difficult it is to learn NEW magic systems. The alternate way of learning magic is through Initiation, which represents an imparting of mystic knowledge through trials/sacrifice/ritual.
The other way around this penalty is through Integration - ie, figuring out the underlying principles of a magical technique, and working it into Hermetic magic. That takes quite a while, but it's the main way that Hermetic magic improves over time.
That being said, the Opening of the Gift is actually a combination of conventional learning and Initiation - a character is 'conventionally' taught the 15 Techniques and Forms in a season, but it's done in a way that allows them to learn them all at once without penalty (ie, Initiation). However, once they've been taught Hermetic magic, each one of those TeFo's acts as a penalty for learning a new Supernatural Ability.
There are magical traditions that aren't penalized NEARLY as much - Folk Witches from Hedge Magic, for example. (They have someothing like 12 separate magical abilities that don't penalize each other.) However, that's explicitly called out as unique to that group. In fact, one of the research opportunities for Hermetics is to try and figure out how they're able to do that. And successful research grants the "Subtle Opening" virtue, which means that Hermetics whose Gift is opened by someone who has that virtue isn't penalized (nearly as much) for learning new Supernatural abilities.
EDIT - oh, also note that non-skill-based supernatural virtues can also be taught...technically. Ie, it's possible to "teach" someone Gentle Gift, for example. However, it's really difficult to do, and these rules exist primarily as a way of justifying how Hermetics can pass on their House virtues to their apprentices. (As such, the rules are set up so that it's relatively easy to learn 1 minor virtue by osmosis or explicit training, but anything else becomes quite difficult to do.)