Does anyone here happen to know whether or not there's any difference between GameCube component output and Wii component output in terms of quality? I'd expect them to be the same, personally, but I'm curious as to whether or not anyone's done a side-by-side comparison to see for sure.

I am not sure, but logic tells me that a Gamecube game on the Gamecube looks exactly the same as the same game on the Wii with component cables.   I don't see how it would change.  I play my Gamecube games on my Wii with component and they look like they always did.
 
On the other side, the Wii games look better than the Gamecube games, depending on the quality of the game itself.

No difference.

I actually thought the component output on the Gamecube was better than the Wii.  I however did not compare the same games.  I compared Fire Emblem Path of Radiance to Twilight Princess.  The only way to truly know is to get Twilight Princess for GC and for Wii and have both consoles hooked up through component cables and tell for yourself.  I guess it all depends on the person and the TV settings.  Because a lot of people say HDMI looks better than VGA for 360, but I prefer VGA over HDMI.