As per the wattage ratings, It would probably
work fine, but as others are attesting, blowing out a PSU is bad for everything else. This is why all the recommendations for buying a better PSU.
Its not that it
won't work ... it will, its just the risk factor is all - the risk that if a PSU fails, it often takes something out with it. The closer you push a PSU to its limits - especially a lower quality one, the risk of failure goes up. That PSU is listed in tier 6 out of 7 (7 being complete trash) here:
https://linustechtips.com/main/topic/631048-psu-tier-list-old/
So I'd say that puts you in a pretty high risk category. A 580 would somewhat lower that risk.
I had one blow out on me after about two or three years of use (for no apparent good reason other than poor build quality) and while my mobo and CPU survived, all my hard drives did not, nor did my video card.
Learned my lesson after that and went with one that exceeded my power requirements by about 100% (and is in tier 1 in the above list). It's getting a bit long in the tooth now (oldest component in my case by a long shot) and probably should be replaced soon, but I got about ten years out of it so far - worth the extra money, I'd say.