No it won't. Try playing Initial D. Sega disabled the optical out so people couldn't pirate the soundtrack - they also hard coded the audio mix so the car sounds were much louder than the music. It totally ruined the game for me.
There are other examples, but they are few and far between, basically.
Hmm... So it appears that it can depend on the game. No matter, then. If two inputs are used, my receiver will use the digital one over the analog one if there's a digital signal. Otherwise it'll just use the analog one.
Since the GC can only do Dolby Pro Logic variations it doesn't need digital out. Seeing as though you are hooking stuff up you might want to invest in an A/V switchbox like Zektor or Audio Authority. The cheap and effective way is Pelican Accesories.
Well, even normal stereo sounds much better with PS2's digital out than with analog. Now Gamecube's analog out is probably better than PS2's, but still digital out would be nice.