Yes. All Wii models (except Wii Mini) are natively backward compatible with GameCube discs.
Some discs show "This disc is for GameCube only" on Wii—ignore it. It's a leftover anti-piracy check; the game will still launch.
Use an original Wii (RVL-001) with component cables, a WaveBird wireless controller, and a 251-block memory card.