Yes, it will support 600W system too, but it will have the run time shorter.
If your system has 350W PSU, it probably runs @ 200W and that will give u about 9 min.
my system psu is of 180 watt. i will buy sapphire radeon hd 7750 1gb ddr5. but that video card consumes only 55 watt. so probably i would be needing 180+55=235watt, about 250 watt psu is needed if i buy that video card. is my calculation right?