Officially it only works with Smash Bros on the Wii U. It won't work on any Wii U games, Wii U VC games, Wii games in vWii mode (including Smash Bros Brawl, which is supposed to have GC controller support!) or any Wii VC games in vWii mode.
But yes, unofficially it will work with
Nintendont, so you'll be able to play GC games in hacked vWii mode using an original GC controller, so at least that's something. (
Nintendont also enables the use of a Wii U Pro Controller, which is otherwise restricted to Wii U mode only, for GC games.) Unfortunately that doesn't make the controllers work with anything else in vWii mode so you'll still need a Classic Controller for VC games.
However, there is another kind of adapter (like
this one from Mayflash, so third party) that will connect a GameCube controller to a Wii remote and have the Wii recognise it as a Classic Controller. Those still work with the Wii U and would enable you to play N64 VC games in vWii mode with a GameCube controller. I'm trying to work out what to buy for my Wii U so that I've got everything covered (Nintendo really need to sort their controller situation out, it's ridiculous, I feel like I need to buy 10 different kinds of controller and adapter!) and I think one of those is the best all-round solution. It would even make the GameCube controller wireless, as it would be connected to the Wii U via the Wii remote's Bluetooth (or, in my case, double wireless as I'd be using a Wavebird!).