Depends on what you mean by "online"...
As far as playing with other players online (kinda like coop, but only online), as far as I know, it's not possible. Of course, if you find anything along those lines, let me know!

What may have confused you is that the Wii version (like all the other versions) connects to the Internet to get other players' tower heights when you're building in WOGCorp. This is about as online multiplayer as it gets. Basically, it just displays other players' towers as clouds in the air at the heights they're currently building at.

Other than this, as far as I know, it's only local coop.

Thanks for this

Cleared up some confusion!

No problem. That's what we're here for.