No, it cannot play Gamecube games. So you'll have to keep your Wii or buy a new Gamecube!
Probably better to keep your Wii unless you use one of the attachments (IE, Gameboy Player or LAN adapter). GCN component cables are ludicrously expensive.
Honestly, I'm keeping both. GCN and WiiU going in the living room, retaining Wii for hacking purposes and all. Like hell if I'm going to give up my custom NSMBWii soundtrack.
Quite a few people are hoping the Wii U will have some Gamecube VC games, upgraded to take advantage of the HD capabilities of the Wii U, but there's been nothing confirmed or even officially said about that idea.
With Nintendo showing no interest in upscaling Wii games, I sincerely doubt that will happen. Some GCN games MIGHT be downloadable down the line, but I don't expect any enhancements.
Speaking of which...do either the Game Pad or the Pro have analogue triggers? The Wii's Classic Controller did, but Classic Controller Pro doesn't. If the WiiU doesn't, then that rules out a couple of GCN titles (Rogue Squadron and such).
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