I believe it would be a bad idea. Official specs say upto 200W, so 6950 / 560Ti is about the maximum reliable cooling capability.
For a GTX 580, IMO you should get either the AC Xtreme Plus II, the TR Shaman or the AF Peter (DC Dracula).
I have an AC Xtreme Plus II pre-fitted on a KFA2 Anarchy. The problem is the fanmanagement. I flashed the card a while ago to minimun fanspeed 10%. But somehow (and I cant reverse it) it has a 20% minimum fanspeed. And its annoying as it used to be dead quiet at idle.
I am currently looking for fix by downvolting. But I cant find the right plugs or adaptors. there for a I need a new custom cooler. I am not very good at soldering
The good part is that the KFA2 Anarchy has excellent VRM coolers and a nice backplate so I only have the change the GPU fan. The AF Peter and the Thermalright Shaman's are good choices, but they are too high block the PCI slot for my soundcard (which gives a much better sound than the supposedly excellent onboard crap).
The mono plus is not too high or heavy, and I have excellent airflow in my case so a good silent single 120mm fan should be enough. A 580GTX is hardly ever maxxed out on most games, so I dont hit 200+W often.