Like what has been said, anything is possible with linux, there are homebrew distros, but they can be hard to find, and running the disc would require a swap disc or slide card.
Emulation may be possible, but running the gamecube specs on top of the playstation 2 software would be difficult, even computer emulators can't get here if I understand.
Using a swap disc and a slide card would probably allow you to do this, although I hear gamesharks are a commodity to be used as a swap disc, so swapping a swap disc would not be too cool if that is what you are considering the gameshark for.