Well, it really depends on the fuel... All race fuel is not the same. The big problem with airplane avgas is that it is designed to burn best at a high altitude, and we don't drive up there... Quite often fuel will allow your car to run better, a bit crisper perhaps, but without a specific tune for it you are only going to achieve minimal results for the amount of money you are spending, with a dedicated tune you can get more, but you really only need it if the engine is built up for it ( turbo High CR etc. )
If it is unleaded it will not hurt your car and if it is leaded one or two tanks aren't going to kill your cat, but I believe it will over time, not sure that is a fact though.