I couldn't justify buying a new Wii just for the color, regardless, but if the opportunity came up, the downloaded games and saves are tied to the console. There is a way to untie the saves using something from Datel IIRC, though.
Really want that. Theoretical question. Since I'm a color whore. I get a new DSi. Is there any earthly way to deauthorize my account on that one and get all my DSiware on the other one? Or do I have to start over?