Here is your answer:http://gigaom.com/apple/new-27-inch-imac-supports-dual-external-display-output/
You will run into performance problems. If you want to know how it would perform, try looking up multi-monitor gaming performance metrics for the following cards (which come in the new imacs):
Youprobably won't find performance metrics for this because people dont try to do it.
These are MOBILE GPUs. Your experience playing across three monitors will NOT be pleasant. The iMac is essentially a large screen laptop. It is not a high performance gaming machine capable of pushing games @ 5760x1080.
While the GPUs in the iMac are perfectly capable of running 3 screens for web browsing, etc... it most likely won't do what you want it to do.
I have the 6970M in a laptop and I wouldn't imagine it being able to push triple screen gaming.
Also, the native resolution of the 27" iMac is 2560 by 1440. I suspect that even the mighty 6970M wouldn't push games well at that resolution in anything other than low settings, for most games.
To do what you want you would need a desktop class card capable of pushing 5760x1080.