I agree that someone from stage management should be in the room, but what I do largely depends on what age group of actors I'm working with. With elementary students, I'll usually join in the exercises and participate with them. With middle or high school students, I'll feel it out at each rehearsal and sometimes join in and sometimes step back and let whoever is leading the exercises be the only adult in charge of those exercises. At movement and vocal rehearsals with students, I will definitely be in the room, helping the actors maintain focus and making sure breaks happen and we stay on schedule.
With adults or rehearsals where discipline and focus aren't an issue, I'll sit in the back and catch up on emails and paperwork. I'll still keep an eye out for things that I could do (getting fans for an increasingly hot room, getting ice packs for injuries, making copies, cleaning up spills, etc). Much of it involves figuring out much the person leading the rehearsal (director, music director, choreographer,etc) wants or needs me to be involved, and in what way.
Regardless of age group, I make sure everyone is there who should be before I do my own thing, and I'll do a general check to see if there's anything else the rehearsal needs before we get started. Also, when I'm stage managing students, I will step out of participating if at any time they need reminders to focus or if there are any discipline problems.