I have a couple third party Wii U GC adapters, one of them is from MayFlash, and they work fine in Dolphin when you configure them manually. Also, I noticed the auto generated controller configs mapped the triggers to the shoulder buttons.
I slightly modified dolphinControllers.py and dolphinGenerator.py under "/usr/lib/python2.7/site-packages/configgen/generators/dolphin" to fix some of the problems. Now, when launching through EmulationStation it'll use the adapter if it's found. Analog triggers get properly mapped as well. Not sure if the ID for each Wii U adapter is the same, but it was for both of mine in Wii U mode.