Hmmmm.... I've not been following Nintendo for that long so I'm not in on any "hints or rumors" that may be out there. While I'm not against wild speculation, I do think that this idea could have been presented a little differently so as to be taken a little more seriously. While I HIGHLY doubt that Nintendo is going online, I can't say it would suprise me.
First, the Gamecube does already have the ability to handle online play. It's about as equiped as the Playstation was when it first came out. Granted, they didn't go as far as Microsoft and throw in a NIC card, but they did at least leave their options open. Microsoft from day one has been upfront the online gaming is a huge part of their future plans (which was not alltogether stupid of them). Therefore, while online play seems unlikely for the GameCube its still as technically possible as it was on the PlayStation.
IF Nintendo plans to stay in the console game (which I believe they will) then certainly they understand that online gaming is the future. Yet Nintendo seems like the kind of company that likes to keep their cards close and watch what everybody else does for a while. Think about it, you've got Sony and Microsoft both fighting to build up online gaming arenas. Both of them are King Kongs in their own right. Sony has the market while Microsoft has the money. If I were Nintendo I would sit back, watch them make their mistakes, and then build my own arena that trumps both of them. With that in mind we can then begin to build what an online gaming arena in the Nintendo world would look like.
First off, I think they will follow MS and build a centralized, closed system. This is what MS did right in that it provides a standard simplified experience for every game. I am an XBL member and I can tell you the experience is awesome. There are some things that you go into every game knowing how to operate. Voice chat is also amazing. You don't know how awesome it is until you frag someone and hear them cry out your name in despair 100 miles away. On the other hand, I think that they will take from Sony's model a little bit and keep pricing at a per/game level. I think that Nintendo would also learn from Sony's mistake and make broadband a requirement from the beginning while following Sony's lead in letting publishers have more control over each games online capabilities.
I dunno. It seems unlikely but I can see Nintendo doing it. They've had enough time to build up the infastructure to do it with, and I like the direction I see Nintendo going. I also think that Nintendo would be super quiet about this and then introduce it with a ton of fanfare. Then again, knowing Nintendo it could just be a cross between Pokemon & Dance Dance Revolution ;-]