I just setup a Pluto Home system (smarthome + media server, plutohome.com, free open source). It
Because of the way that the Gamecube is built opposed to that of a normal PC, the Gamecube isn't really fit to run anything like this. You would at the very least have to find a custom modchip that would enable you run the system, for Nintendo certainly isn't going to leave the door open that much for you.
The Gamecubes purpose is to play games...not turn on your sprinklers. So I doubt you'll be getting anything along those lines to work with a GC. If you somehow manage it; more power to ya.
True, the Gamecube is a mini computer. But I think its a little bit too mini for what you're suggesting. You could try it, all it should have inside it is a hard disk, graphics card, etc (I don't actually know because i haven't taken mine apart). Plus I don't know if you could plug in all the things your suggesting either. Its just too incompatible. You could try, but I'd get an old, cheap, regected one and take it apart to see what's inside, but I think its just a little be too different from a computer.