Some games will work fine on dialup. It depends on how much data the game needs to send from player-to-server, and server-to-player. I would guess that games like RTS and Puzzle games don't require much bandwidth. Games like FPS with physics engines and large environments, vehicles, lots of players, etc. (Battlefield 2 for example), will require broadband of some kind.

You may get lucky though, and it may be that the Wii games don't require much bandwidth for online play. But you'll have to wait until it's released and try it for yourself.