I can tell you from experience that Office 2011, like Ofc 2008 before it, has a registry key setting that looks for any other versions of Office running on the same network and if it finds it will force all but one instance of Office to quit running. I'm not exactly sure how they do this, but they do and it is fairly effective against casual piracy.
Now that said, as long as you aren't running simultaneously on the same network, you'll not run into this conflict. Read into that what you will. ;-)
If you want to stay 100% functional on 3 computers running on the same network simultaneously, you can buy a single-user license of Office for Mac. Our vendor (PC Connection) has them.