You mean networking your gamecube to a pc and back your games up? Or play your backupped games (the ones on your harddisk) on your gamecube with a gamecube->pc link?
For the first, I don't think so, not without a hardware hack, I think that is secured. And you need a piece of software for your gamecube and pc as well.
Second: Probably, but not without a piece of software for your gamecube.
Be aware, this a all pure theory, I don't have a gamecube, haven't seen any software, nor have I seen a working pc-gamecube link. Plus, I don't think this kind of questions are allowed on this board.