The unfortunate news have been revealed which mentions that the Wii U GameCube adapter is only usable for Super Smash Bros. Wii U but there's a chance that Nintendo could change this in the future with a new firmware update.
Source: http://store.nintendo.co.uk/wii-u-accessories/gamecube-controller-adapter-for-wii-u/11028551.html
In a way this is pointless to own because you can't even play Wii U games with it much less on the Wii Mode, though for Super Smash Bros. it works.
Very disappointed once again, Nintendo.