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.