Wii U Gamecube controller adapter only works with Smash Bros.
Speaking with Eurogamer Nintendo have confirmed that the only game to support the Wii U Gamecube controller adapter with be Super Smash Bros. Wii U. This means that the adapter won’t allow for use of the Gamecube controller to play Wii games through the in built emulation, or any other existing Wii U titles.
Compatibility with the Wii emulation seemed like a no brainer to me, and using the adapter to offer Gamecube titles on the Virtual Console would also have been neat. Hopefully Nintendo can add this in a future update, but at the moment this is not in their plans.