No it isn't compatible. Once the Wii is inserted with a GC game, it turns into a GC. Meaning that only GC accessories will comply with it.
Correct. Always keep in mind that anything that's Wii about the Wii shuts down once you launch a Gamecube disc. That means you won't be able to use Wiimotes, anything that plugs into the Wiimote, Wifi, internal Wii's memory, USB devices, nothing. Just Gamecube controllers, Gamecube Memory Cards and the Gameboy Advance cable.