GPU mining (should) barely use any CPU at all. Latest startup on my windows poclbm-mod miner has poclbm using about 8 CPU minutes over about 9 hours. Compare that to task manager using 15 minutes in 3 hours, and IDK how much in chrome/etc. It barely even uses 1% of the CPU, the bitcoin/bitcoind probably uses more CPU to handle block processing.
As for if a 1kW PSU will be enough, and how efficient it will be, depends ENTIRELY on the PSU. Remember most of the load is going onto the +12V rails in that scenario, and so the PSU has to be appropriately sized. I've a 700W PSU that has PCIe connectors but can not have more than about 375W across both +12V rails on the PCI-express connectors (200W on one, 175W on the other rail) so it would maybe run 2 5870s. I've another (newer) 400W PSU that can actually do almost as well (18A on either +12V rail, but a combined total of 350W). So really, you have to see the plate on the PSU to be able to have any hope of telling. That said, most of you're big 1kW+ PSUs are designed pretty good and heavy on +12V these days (unlike my 700W example)