I recently declined to do a gig 'in the round' because of questions like this, but the promoter seemed more than happy to drop the idea, which had been suggested by one of the other acts.This also begs the question of which way the musicians will even face. Will you turn around regularly? Or will the dancers be moving around the circle? It wouldn't be very nice if half the audience only ever sees your backside.
Unless there is an outlet or two in the floor in the center of the room, there would still be the issue of sending at least one power supply cord to the room's center. Maybe that could be done via the ceiling, however.