Eyefinity is surround gaming. You can't use it with different resolutions for one, so your 1920x1080 monitor would have to run at 1600x900 and look off not running native. You also need all 3 screens to be the same physical size or else things don't line up when you go from 1 screen to the next. Lastly, you want 3 identical, very thin to no bezel screens so when they are together there isn't a seam in there. You wanting to play on a TV in the middle with 2 on the sides won't work. Well, it would work, but would unplayable. Imagine your TV is 32" say for example and the monitors are 21". So when someones head it at the top of the 32" screen and they turn left, all of a sudden, it's at the top of the 21" monitor and 11" down from his head was a second ago.
Now if you want 3 screen, to game on 1, and have the other two running, yes, you can mix and match any 3 screens you want and game on 1.