Are CPU karts immune to physics?

Yes. Super Mario Kart is a pretty typical example of a cheating computer. There's even a term for this - "Rubber Banding." Rubber banding is a way to balance game difficulty. The AI will always catch up to you, regardless of how far behind they are. The intent is to keep the game close without having to program a complex AI routine for driving the karts.

TV Tropes even uses Super Mario Kart as a prime example of both "Rubber Band AI" and "The Computer Is a Cheating Bastard" tropes:

They also out right clip through course obstacles like Thwomps and pipes while you need a Star to smash through the same things yourself. The only thing they they can bump into that slows them down are the walls and that's if you push them hard enough into a wall.

So yes, they cheat. Blatantly, obviously, and unfairly. :) This is an issue in many games - even recent ones. In Saints Row 3, for example, the AI can drive trash trucks like they're sports cars if they so desire. They can also speed up to intercept you when you're driving the same car as they are, and you've got the throttle to the floor.