Airez
I believe it's highly unlikely that this will happen. While GAIA has put up some games off-site in the past (Word Bump into Newgrounds), it's unlikely they'll make the Battle System compatible with the Wii. It'll most likely be site-exclusive.
Site exclusive? Well funnily enough the site can be accessed on the Nintendo Wii and most games would be playable if it weren't for the latest flashplayer being needed, which the Wii doesn't have (Although may be updated in the future). All the games simply require a mouse and a working left click, which the Wii can offer.