It looks like you can use Pro controller for 2nd 3rd or 4th player just 1st player has to be gamepad.
Here's some info that should help
Multiplayer is supported, GamePad will always be Player 1, you need a Wii Remote with either Nunchuck or Classic Controller or WiiU Pro Controller connected for Player 2, 3 and 4, the Wii Remote by itself will not work as you will have 4 solid lights on the bottom of the Wii Remote. Nunchuck is not recommended because the lack of buttons available for mappings.
If you have the official or 3rd party Gamecube USB adapter with the 4 ports, this ONLY works if you select NO for GamePad mode, you still require a Wii Remote to select either to play on TV or TV and GamePad. With the GC USB adapter you can still connect/use Wii Remotes+Classic Controller at the same time.
If your short for $, The el cheap 3rd party eBay special adapter works, so no need to get the official one.
Added Notes: There has been reports that not all cheap 3rd party GC USB adapter will work, if in doubt, spend that little extra and grab the Mayflashversion as this is known to work.
Make sure the GC USB adapter is connected to the FRONT USB ports next to the SD CARD and make sure the switch on the GC USB adapter set to WiiU.
To exit back to the WiiU menu while using the GC USB adapter, press the following buttons on the GC controller: L + R + Z + Start