Due to altitude, the speed of sound at Bonneville is likely to be more like 750mph, maybe slightly less depending on the weather.
The question of sonic flow on the wheel is an interesting one. The displaced air accelerates over the wheel such that its peak speed above the wheel is significantly higher than the speed at which the car is travelling, but the air the wheel is hauling around with it only has the wheel speed right at the wheel surface. There will be a mixing zone between the wheel surface and the air flying over the top, but it's hard to say what will happen there, if there will be any actual supersonic flow. I would doubt it. Googling supersonic cylinders might throw up some information on what could happen though!
You would never hear a "sonc boom" from it alone though - that's created by a completely different mechanism.