I'm curious if anybody knows or can estimate what would happen if I were to swap an IC from a SNES cart with one from another game?
Would something interesting happen or would it simply not run at all?
Depends. Some SNES carts had a security key that did something with the checksum of the game ROM. I know that with some you can blow a new image onto an EPROM or flash chip and drop it in, and play a different game.
You probably want to look at the SNES homebrew scene for more advice.