Maybe, Depends if Diablo 3 will work on Windows Server 2008+? If so then it should run on Windows MultiPoint Server 2011 with LAN thin clients. Granted you'll still need 7 purchased copies of Diablo 3, because the game requires log in sessions, with disc code authentication for each account.
So I suppose the real question is does Diablo 3 run on RDP?
Other option could be a windows 7 premium install, and a ugh... think its call vrm something, but it allows you to create virtual machines. You have to download XP Mode for windows 7 premium or ultimate. Then if you have several GPU's with multi-mon you can several instances of diablo3 on one machine. But again you'll need a license for each VM.