Since no one else has commented on this, it seems likely that things may have changed since I went through UPT 100 years ago; but....
When I went through, we were explicitly prohibited from outside flying, and it didn't matter if you had never flown before or commanded the last Space Shuttle mission, or anywhere in between. You probably want to know the status of that before putting any irrevocable planes in place.
Yes, I realize any such prohibition is likely unenforceable if push comes to shove. Consider, however, the BS that the AF wraps around "high risk" activities (among which it lists GA flying), and which AETC enhances. As a student in a program that will determine the shape of your entire professional life yet to come and which will likely be the toughest undertaking you have yet experienced... do you really want to get in that fight?
Again, my information may be woefully out of date, but, I'd check if I were you....