Do you really want the issues that seem to come from these eyefinity setups.
Low FPS, Lower Settings, frame latency and stuttering.
One 7970 can barely run Tomb Raider at full above 40fps on 1900x1200 on my PC. Why would you want to try it with 3 monitors?
I love how you interjected your opinion while not answering the OPs question. I have to say, that isn't surprising. Anyway - Personally I will never use a single monitor only ever again. Dual monitors are fantastic, even if you're not in extended desktop or surround mode you can use the secondary screen as an accessory to display to do various things such as skype, chat, browser windows, I could go on here. You gain a lot of functionality with additional screens even if you DONT go into surround mode - I find that most detractors simply haven't used it.
For instance, when I played world of warcraft dual monitors was a godsend. Anyone that has played that game knows that skype is vital for arena play at the high end, and programs such as vent or mumble are critical for raiding. With dual monitors you can handle all of that stuff on your secondary monitor without tabbing out of WoW. Furthermore, if you want to view a youtube offscreen without alt tabbing you can do that. If you want to do anything on the accessory display you can do that. My opinion is that 95% of people who are detractors haven't ever used more than one. Furthermore, multi monitor isn't ONLY for extended desktop or surround. Heck, you can use single monitor for gaming while doing a plethora of other things on your accessory screens. I simply can't see anyone having used monitors in this manner not liking it. It is very convenient. So the argument about not liking surround for certain things? Yeah okay, but you don't have to use extended desktops. Nobody can deny the benefits of additional screens even if you're not in extended desktop or surround mode. The benefits are even larger when doing anything productivity related. Having that much more real estate is simply fantastic. Again, not surround or extended desktop - those aren't pre-requisites to multi monitor. Just being able to have a browser window open on one screen, word or powerpoint in another, and a youtube on a third screen. It's awesome, I love it. There is no single monitor that can give you as much real estate for productivity or fun as will having multiple monitors working in tandem.
Anyway, the answer to the OP is yes. It will work. I don't think this thread was created with an intent of asking for a million opinions on surround, even if I fell into the trap of doing the same thing. Anyway, short answer is yes OP.