12V rail is 53A, which means 636W on the 12V rail alone.
@Bucknutty: I don't understand what you mean when you say it is not the wattage but the current? V*I=W
Maybe that was not the best way to experess my thought.
Although the math based on the advertised wattage says the amperage should be x many times the PSU is rated at far lower. You could simply assume that 650/12=54.16 amps. but that may not be true because the PSU may use cheap parts, or the arrangment of 12v vs 5v vs 3.3v may make the usable wattage of the PSU much lower than advertised.
I did not look it up the PSU in question when I made my first statement. I was hoping the OP would.
The math suggests that each video card 220/12=18.3 so both video cards should be 37 total.
I7 is 77w part so lets say 77/12=6.5
We are now at 44, not including the board ram fans and drives which should be tiny in comparison. Lets say 6 amps to make the math easy.
We are now at 50.
This math suggests it might work. Lets look at newegg say and see what the PSU Specs are.
3.3V@25A, +5V@25A, +12V@53A, -12V@0.8A, +5VSB@3.0A
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020
Its close but it should work.
Here is a PSU that is advertised as 680 but the amperage ratting is very low.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817148022
+3.3V@38A, +5V@40A, +12V1@22A, +12V2@24A, -5V@0.3A, -12V@0.8A, +5VSB@2A
The math here suggests the PSU only has 552 watts on the 12v rail, Much lower than the advertised wattage of 680.
I guess I should have said looking at the advertised wattage is not issue to be concerned with. You should look at the actual wattage and amperage.
In conlusion I think this system will run fine. Some one check my math...and my logic... it has been a long and confusing day.