No — GameCube controllers cannot navigate the Wii System Menu. The Wii Menu only recognizes Wii Remotes (and Wii U Pro Controller on Wii U in Wii Mode).
On Wii U (in Wii Mode), GameCube controllers require the GameCube Controller Adapter (for Super Smash Bros. for Wii U) and only work in supported titles — not the Wii U Menu or Wii System Menu.
| Context | GameCube Controller Works? |
|---|---|
| Wii System Menu | ❌ No |
| GameCube Game Playback | ✅ Yes (RVL-001 only) |
| Wii Games with GC Support | ✅ Yes (check per game) |
| Virtual Console / WiiWare | ❌ No |