Very unfortunately, NSMB Wii will have no wi-fi capability.
The reason? "The Wii is being pushed to its limit with this game..." so basically, that means no wi-fi. The question that begs to be asked: What the hell does NSMB Wii have under the hood that's taking up so much space that wi-fi is not a possibility.
Mario Kart Wii seems more technically extensive and it had wi-fi and had to keep up with all kinds of madness happening on-screen with minimal lag. Brawl is most likely 10x as technically extensive as NSMB Wii, yet it had wi-fi capabilities... yes, it sucked, but it was there, at least.
Just... I don't understand how the system is "being pushed to its limit" and can't support it with a game that looks like a polished up port of NSMB (unless there are like 50 million levels crammed into the game).