The official Air Force Academy Band is not made up of cadets. It is permanent party enlisted whose only job is to perform with the band. They are the ones who you will see in parades and ceremonies.
The opportunity for cadets is with the Drum and Bugle Corps. It is not competitive and they recruit from all of the cadets and take anyone willing regardless of experience. It is, however, highly demanding of time and from what I have seen a majority of people who start out in D & B do not continue. Of course, there are exceptions to this and many enjoy the high tempo of activity. I am not sure of the poster 2011's Mom still visits this forum, but her daughter was the Drum Major for D & B and she would have more information if you're interested.
To answer your original question, no, the band directors wouldn't have any pull for your admission.
Stealth_81