Yes. It might pull a few more watts than the stock version.
When they recommend a power supply wattage they assume you have a very cheap power supply as well. Meaning that you have a PSU that will put out a peak of 550 watts. A quality power supply from one of the brands listed above will put out it's rated wattage continuously not just peak.
If you can afford it just get this http://www.newegg.com/Product/Product.aspx?Item=N82E168... it more than you need but gives you breathing room Knowing that a good power supply can last you many years, you want to think about possible upgrades to your computer system in the future, to make sure that your power supply can handle the load with that new part.
I agree and it boils down to the amps on the 12v rail. nVidia suggest to be safe for the normal card to use the 550w PSU. I have see other PSU's in the 450w range push the 680.
But since yours is OC'd then it could still be the 550w. You have to realize that the 680 draws less power than it older brother the 580. So you might be able to still use the 550w PSU but just make sure you get the PSU that states constant power not peak.
But it is up to you if you feel safer with a 650w PSU then go with that. That card is a lot of money. Good luck.