Will Rehearsal Live Share work for instruments other than voice?
Although voice is the easiest instrument to demonstrate the capabilities of Rehearsal Live Share with, it's absolutely not the only use case.
There's no reason you can't teach a lesson or hold a band practice using RMS Creator and Rehearsal Live Share. A few things to consider:
A MIDI track will be necessary to keep everyone in sync. So, you as the band director could use anything from a simple MIDI percussion click track you've created, to a fully orchestrated MIDI piece. Do you use notation software like Finale, Sibelius, or Notion already? Maybe you prep all of your scores in Garageband or Logic? You can export pieces made in any of these softwares as MIDI files, import them into RMS Creator, share it with your band, and everyone will have something to play over.
Just like with the vocal application, only the Director would hear all of the parts. The students would only hear themselves and the click or midi instrumentation track you've prepared.
A limitation you may run into are the mics your students may use. Note that, while the internal mic of their laptop may pick up the human voice just fine, it may not translate brass or winds or percussion properly. In those cases your student may need to purchase a higher quality USB Mic - which luckily are fairly affordable and readily available.