Yes it will on a good 600W PSU. Unfortunatley that PSU is very bad and I wouldn't trust to run my system at all. Consider upgrading to a Corsair CX600 or other reputable brand. Here are the good ones Corsair, OCZ, PC Power & Cooling, Antec, XFX and Seasonic (listed in no specific order). I recommend the CX600 because it's the cheapest good one that can handle what you want.