It depends what kinda power supply, if its a cheap chinese power supply, it probably doesnt even put out 18A. If its a seasonic, antec, or another quality manufacturer, it might be alright, but i doubt it.
My uncle couldn't run a 8500GT on a 18amp PSU which is 21amps for the card with a similar set up as you...9600GT.................................400W .........................26A
At this point even if its a Corsair 18a PSU your not meeting the power requiments at 18a.
The only card I see you might be able to get away with is 8500GT.......300W ......18A or the 8600GTS..........350W ..........18A
Well yeah you can "run" it...but your not getting half the power the GPU can dish out. Plus the extra side bonus of overloading the PSU for a possible PSU failure that kills your system.
Just telling you what it says...you can decide what you wanna do.