I have a 7950, and yeah I am able to run 3 at once, after I got the active mini-DP adaptor and cable for the 3rd port.
Will there be an issue with 3 VGAs (analog), not 100% sure, you will be a nice test case, please let us know here, all 3 of mine are digital.
I am hopeful, it's not a problem.
If anyone else has done this and reads they will surely chime in *hint hint* muhahaha!
OP, with those smaller screens, I see why you want to do this, I use 2 only usually, 3rd is my 39" HDTV, and not exactly placed right in my face, like my monitors: I have a portrait monitor 24" and a regular 23" and spaced apart, so I don't spread my games across them, it's very dependent on the software supporting it anyway, otherwise I'd expect it be quite distorted stretched artificially.
Perhaps someone doing it, can back this up or refute.
I do game a bit myself, but never needed that much range, but my eyes are getting old, so jumping around mega quick focusing over and over isn't as good.
So 1 it is....
Time machine would be nice, but I'd go back 25 years or so, ooops no FPS! muhahaha!