If I were to play a Wii game on the Wii U, could I play it on the tablet? Using the tablet as the display and use the normal Wii controller+nunchuck to play the game? Or does that not work for some reason?
Now the answer for this question is Yes (with additional conditions though). Latest system update (September 30, 2013) allows all Wii games to be played on Wii U GamePad controller, however original Wii Remote controller is required for games control. Reference.