probably if you don't overclock anything it will be possible to crossfire them, but the question is for how long, it will probably be using your cpu wattage almost 100%, so yes, if you want a stable crossfire i would be looking for a better psu. a good corsair 750w can handle them perfectly for a long time, now the HX650 can give you problems in a short time period.
The 650 watt PSU is enough to power and OC them if you want becaus your total system power draw not just the cards but your whole system is 470w on load. One card on load draws 180w.
When in CF you second card does not draw the same voltage as the first card does and if you ever have it on the screen while playing you will see what I am talking about.
The PSU you have now is a Tier 2 which is a good place to be. As long as you are on Tier 1 or 2 you have nothing to worry about. I will link you to it. You still have room to OC your i7 also.
So for now you are good to go. There is one other thing. It all depends on how many amps are on the 12v rail. So the one card needs 15amps for your whole system you would need 39.17amps.
Your PSU has I believe one 12v rail and it is 52amps and that is not counting all the little voltage on 3.3v or the 5v. So the bottom line you have more than enough power to run the two cards and OC them along with your CPU.
But if you want to fork out a $100.00 to $150.00 for a new PSU then that is totaly up to you. All am doing is giving the facts to the question you asked. So I want to wish you good luck on your CF'ing. Cheers