Question: does suspending the trainer mean the horse can’t run?
No, to keep Medina Spirit from running, Pimlico and NYRA would have to do what Churchill has done, which is Baffert is 'ruled off' the grounds, meaning he can't even run at Churchill in his assistant trainer's names and his horses must vacate the grounds.
Apparently whoever didn't fly back to SoCal last weekend will be vanned to Pimlico tomorrow with Baffert's Medina Spirit and Concert Tour.