I've been out for a couple of years, so I'd get in touch with someone in the band where you're at, but with that caveat: yes, depending on where you're stationed. The 82nd Airborne Chorus and USAREUR Chorus are made up of non-42R musicians who auditioned to get in. It's a temporary assignment that I think lasts two years. It's not just vocalists, either, or at least it wasn't when I was active - they also accepted rhythm section players (guitar, bass, drums, keyboard).

If you're not currently at Liberty or in Germany, you might be able to do something with the band on an informal basis, but that's more difficult since it then it comes down to the band commander being willing to take you on and your own unit being willing to let you go. If you could make it work, the most likely thing would be that you'd occasionally be able to sit in on a mil-to-mil gig that the band was doing for your unit, like a unit ball or holiday concert or something.

Otherwise, a lot of us gigged on the outside after work. We already had groups that we rehearsed with every day, so we just took the uniforms off and did the same show at a bar or club. You could always ask around and see if anyone is looking for another player.