Based off of what I can find on Q6600 benchmark performance, it can handle a GTX 580 with no performance hits in 3DMark11:http://3dmark.com/3dm11/354176http://3dmark.com/3dm11/304887http://3dmark.com/3dm11/360072
Only look at Graphics score since Physics scales with CPU and I'm comparing an OC'd i7-920, OC'd Q6600, and an underclocked Q6600. It doesn't seem many Q6600 owners overclocked the 580 though. In your case, overclocking it would be useless since the GTX 580 is right at the x8 bandwidth (or x16 on PCI 1.X) limitation.
You can search for your own setups here: http://3dmark.com/search
But can your PSU handle a GTX 580?
In my opinion, if you're gonna upgrade part-by-part, it it wouldn't hurt to start with the case, PSU, and HDD (or SSDs/RAID setup).