Is that an Antec TP 380W? If yes, then I would try it with that PSU and stress it with 3DMark run. If the PSU is insufficient, then you might get instability issues or reboots. What are the rest of your system specs? Include all optical and HDD...
I have been running an evga 7800 GT ocd in my dell 8400 with the stock 350 watt psu. I have more items, ram, 3.2, sound and capture cards, than you, and am having no problems whatsoever.
288 watts is the highest consumption I have recorded, running BF2.
DC Output ......+5V.........+12V.........+3.3V........-5V........-12V.......+5V S
Max.................35A..........24A............28A.........0.5A........1.0A........2.0a
Min...................0A............0A .............0A...........0A..........0A...........0A