As I've mentioned on here (somewhere) previously, I used to play for such classes years ago when a student and what I played included some improvisation and some existing music; Tchaikovsky certainly featured among the latter, though not necessarily always from his ballet scores - I seem to remember that pieces from The Seasons cycle came into it. I certainly had no previous (or subsequent) dance training and, as I mentioned before, I found the whole experience quite puzzling and could never perceive the relationship between what the students were doing and what I was doing. My recollections of the details are pretty hazy at this distance in time, however and it's a long while since I've played at all now, so it was almost part of another life, really.
Best,
Alistair