My point was just that GameCube mode on a Wii can't make good enough use of Bluetooth (used to connect to a Wiimote and, therefore, that adapter) because it doesn't have enough space for the programming code needed to interact with it.
I was understanding that OP was assuming that if you popped any GC disk (burned or retail) into a Wii U in Wii mode it would know what to do with it (and have a built-in GC mode to handle it). I was saying that EVEN IF that was the case, controls would be a problem when the only plugs a GC game knows to look for (in their original place, not attached to a Wiimote or USB port) don't exist on a Wii U.