Sounds like it might not, on the 480i the 'i' stands for interlaced. Check your manual and see if your TV supports or an option for 480p, that is what the GC outputs.
You should still get the component cables though, you can still use them for interlaced signal, I do. Especially since you have a HD TV, I am envious, you REALLY need these cables. What are you using now, RCA? Please say you are not using RCA on your HD TV. S-video, that would be OK.
You may also want to check your manual and see if your TV upconverts to a progressive signal, my friends widescreen panasonic does automatically.
The best place to get the cables is directly from Nintendo, they are the cheapest and fastest way. They do not sell the cable retail.
Hope I was some help.