Possibly but I doubt it. The Wii's multi AV outputs composite, S-video, and YPbPr (analog component). It's most likely taking the component signal and upscaling it. I wouldnt imagine composite upscaled looking good. S-video would be better, but still not outstanding. The issue with the GC is that it's multi AV can only output S-video and composite. Some GC's have a digital AV port, which outputs a YCbCr (digital component) signal. The issue is that it uses a proprietary connector, so you would have to solder to the pins to get a signal. That is because there was only one cable made for the GC to output component, and they are rare and expensive. The signal the GC outputs can't be used without coverting it to analog, and that cable has a chip that does just that. No one has found a solution to mimic that chip sadly. That's why I don't think this will work on the cube. Could be wrong though.
However, I may have found a way to obtain a component signal from the GC (as well as the SNES and N64) using the multi AV port. On the GC, it won't allow you to run games in 480p like that rare cable does, but only certain games supported that feature anyway. It will however provide the best picture relative to the digital AV cable because it will have better color separation than S-video and composite. This should also allow for a sharper overall image. I plan on working on this soon, and posting progress here.