Previous Starcraft games already implemented what you are talking about. You had to have a legitimate serial number to connect to battle.net and play online. It prevented pirates from playing online in any of their servers which would involve any competitions and the like. Sure (just like with SC2) they could create a reverse engineered server and play online, or they could do LAN or local play...
I don't see this method decreasing piracy significantly, especially not as significantly as it'll decrease actual paying customers. Without LAN play I have no interest in the game when I was previously looking quite forward to it. Especially if I have to be online to take part in solo offline campaigns.