Yes, the Gamecube outputs 480p in "progressive scan," and 480i otherwise. When you switch to it, you should see either a bunch of garbage, rolling screen, or nothing at all, assuming the display is 15kHz only.
NES is 256x224p, same as most SNES games. TV's that support 480p will stay be able to display it, but it usually won't be that native resolution anymore, it will be scaled by the TV. If you can still see distinct scanlines exactly between each line of graphics, you can be sure it's actually displaying the native res, which will be the case with a 15kHz-capable display. However, if you can't see the scanlines, that doesn't necessarily mean it's not displaying native res. On some older display the dot pitch is just too coarse to leave that space in between lines (picture is clear enough). If the dot pitch is very fine, you will still be able to see faint scanlines even if it has been scaled up, there will just be twice as many of them and they won't all be in the right places. After you've become familiar with proper scanlines it becomes very obvious what to look for, but if not the 480p test is much simpler to interpret.