A prop at the front of the aircraft bites into undisturbed air, but there will be a boundary between the accelerated air from the prop and the ambient air that the airframe is flying through. I suspect this will the source of significant engineering challenges in dealing with these different supersonic flows and the interactions between them.

A prop at the rear cuts into disturbed air, which, at supersonic speeds, would probably present some design challenges too. The advantage is that the thrust doesn't have to interact with the airframe. I remember reading, when I was a kid, about the intial design of the rear-engine BD-5 having problems with airflow interactions bewteen the propellor and some control surfaces ahead of it.

This got me thinking about my old Cessna 185. It was on floats, and was equipped with an 86" propellor that turned at 2850 rpm for takeoff. That yields a tip speed of 729 mph, or ~Mach 0.96 at sea level standard air pressure. Between the engine and the prop, it was an incredibly loud machine.