Late to the game, sorry, but I was looking for updates on your S's audition process and found this thread.
The audition announcements with which I'm familiar usually specify accompaniment and if recorded will say who is responsible for providing the boom box. If he's doing an improvised solo, I'm sure the professor would want accompaniment so he/she could hear it in the context of the chord progression.
For many years, the standard accompaniment for jazz was the Jamey Aebersold play-a-long series. Lately, Band-in-a-Box has become a popular alternative, as MarkBass pointed out. Not sure I'd want to use "Kind of Blue" as a backing track for fear of being compared with Paul "Mr. P.C." Chambers (Miles' bassist).