Now, granted, I don't teach at an AVID school, but I have been to and observed several schools that use AVID.
For one, it seems to get the greatest benefit in low SES areas. I've seen schools that should be off the rails as far as student engagement and management (based on indicators like SES) that have students that are really taking the initiative to be respectful and attentive to their teachers, and performing at a high level.
The main thing though, is implementation. It is not, as you say, trying to shove your round peg into a square hole, unless it is being implemented incorrectly. No one in education would buy into a system that didn't flex to the needs of the student population. I know the STAAR test doesn't, but that's run by politicians, not educators. It makes a difference.
Finally, good teaching is good teaching. It doesn't matter if you're teaching Calculus or Underwater Basket Weaving. Does every single educational strategy apply to every single class? Absolutely not. But some do, including your band class. The best band directors are out there learning how to be BETTER TEACHERS, which transcends subject matter. Is it possible you could get out of your own way and learn something from AVID rather than complaining?
The the OP: Could it hurt? Outside of losing some personal time, is it possible you could learn something you didn't know, and thereby serve your students in your band better? If so, then it's worth it.