The GTX 580 at max draws 26A on the +12V rail. http://forums.atomicmpc.com.au/index.php?showtopic=264
Your PSU has 3 rails rated at 19A each. Since the 2 PCIe power cables probably each are attached to a separate 19A rail, that would allow for 38A total. But even then, it depends on how the rails are internally wired and protected and how much else is on those rails. But they definetly would be too weak if you decided to add a 2nd GTX 580. While the quick answer is, yes, the PSU will work fine... I would consider moving up to something at bit stronger if you plan on going SLI some day. And one with a single rail or 2 high amp rails.