Yeah they do, but it's really hard to adapt to the GameCube controller layout for it. I don't have a classic controller, though, so maybe that's a better option.
Also note, even though you can stop playing in the middle of a level with the VC, it doesn't mean you should. Not for honor reasons or anything, but because you'll be totally unprepared to pick the game up again when you come back. My VC version is stalled out on level 13 for that very reason.