I don't know dude, that is cutting it VERY close. I would bump up the PSU to at least 450 watt, with only a 300 watt PSU your PC would probably fry itself due to little to no power. The 6670 probably uses little power when it is idle doing nothing, say your looking at your desktop. However when you start to play games it requires more power as it is working harder. So probably no, it wouldn't. If you don't give a PC enough power then the PSU can fry, along with other parts.