You need a cd key linked to your battle.net account, so it should be to play. I'm sure it's realistically more like a few hours. (800,000 preorders in US alone)
Well, SCBW has had 11mil worldwide, so it still has some catching up to do. Even still, rather impressive, and I'm eager to hear the numbers for other regions.
I logged into battle.net and went to scII and that's what happened. I bought a hard copy of the game but haven't installed it. I'll report back in the next few hours.