Can I play Gamecube games with the Wii Classic Controller?

I was looking for N64 games on the Virtual Console and they show icons indicating you need to use either a Wii Classic Controller or a Gamecube controller. Can I do that backwards; use the Wii Classic Controlle to play Gamecube games?

Let me know. This is getting complicated and none of those Gamestop peoples even has a Wii yet.