The gamecube does have a digital output but I am unsure whether it can carry any sound.
The component cable fits in the digital output and carrys a component picture only you still have to have your normal AV cable left and right phono plugged in for the sound.
The GC can indeed output a matrixed version of DD5.1 through its normal AV out which is Dolby Pro Logic 2.(which sounds superb).
Your amp must have DPR 2 decoding onboard to listen to this format.
Now with the GC and Xbox gaming Graphically and Sonically is the best it has ever been but remember better graphics and sound do not make a better game?