MARIO wrote:
They do not work in Wii mode or other games unless the game specifies that it supports them.
As far as I can find, it actually hasn't been stated that the Nintnedo Gamecube Controller Adapter for Wii U won't work in the Wii U's Wii Mode. It hasn't been confirmed it will though either.
The product page for the adapter on Best Buy's website states it will, using the text "Enjoy your favorite titles, including Super Smash Bros. Brawl, with the familiar GameCube controls you know and love", but of course, who's to say Best Buy's listing is correct.