Not sure, but I've got an 8800 gt 1gb in mine that can run it at full with full OSA where the only slowdown I get is because of my cpu
I have a friend who has a 256 like the 7600 and he can run it with little or no slowdown on medium graphic settings although I'd suggest that you turn off shadows altogether. They're not all that great anyway unless you have them cranked to full.
But as for the 7600 gt Not really sure. The main thing SupCom eats is CPU processing so if that's fine a 256mb video card should do fine. Unfortunately, I am by no means any expert on the subject, so this is just my educated guess.
Hope it works out for you. :)