As but a humble student ppl I am not too sure of the physics involved, but I would from a common sense position think that if the prop exceeds the speed of sound, then rather than pushing the air backwards to gain forward thrust, the supersonic prop would actually move the air in a different direction or not move it at all.
I have read that a supersonic prop can result in a loss of thrust. 30% springs to mind for some reason.
At the end of the day, the original post was about NOx, and although a nice idea, in practice silly if not downright dangerous.