I don't think this questions has been asked before: while binding the familiar, it seems it has to spend the season in the lab with the magus. Thus, does the familiar gains exposure experience during this season, and if it does, in what abilities ? Magic Theory ?
The question may have a different answer for the season of binding it for the first time and for a subsequent binding season (to improve the cords).
For the subsequent seasons I'd say it can have exposure to Magic Theory, but not for the first season when the binding is created.
My answer would be functionally the same but I would see it as the familiar, assuming it is already Intelligent rather than having animal cunning, could earn xp or be trained in MT during the initial season but during the initial season of binding an intelligent animal is (I assume in most sagas) definitely a magical being and would therefore subtract its might from the study total so would gain no xp from exposure (unless its might score was only 1) and would be unlikely to gain xp from training as the total for that is unlikely to be higher than its might. After it is bound it definitely has intelligence and does not subtract its might from study totals so would gain exposure if it is helping with the process or could be trained in that season is for some reason the magus would prefer them to not help and was training them instead. One possible reason a magus might not want the familiar’s help is if the bonus would push them into a new vis cost level and they could not handle that much vis.