Yes it should.  And those 1000 watt amps you see at walmart for 80 bucks should be able to push out 1000 watts but they don't.  PSU's are not intended to run at 100% load for hours on end.  Get a good one next time; Corsair, Seasonic, Antec are all good brands.  Coolermaster, Thermaltake, Rosewill and the like are just asking for trouble in a power hungry setup.