It will probably work, but i'd get a new PSU anyway.
With OCCT software which completely maxes out the power load of two 5870's (the largest load they could ever possibly experience), the load power is 664 watts with Crossfired 5870's on a i7 system.
It's extremely unlikely any game will use that amount of load power though, no matter how demanding. Just about any game will not draw more than 500 watts at the very very most on the same setup. So you should be ok for gaming. If you never run something like OCCT or furmark which draw more power than any game will (by atleast 100+ watt), your'll be ok.
Bit off topic but OCCT will crash a 4xxx, and 3xxx ATI card - it draws so much power it overloads the card. AMD/ATI moved to hardware based overcurrent protection with the 5xxx series. Something they should have done ages ago.