600W Power Supply Enough?

Not really, but I would not SLI those GPUs.

256MB 8800GTs are underpowered. The thing that is most holding up your gaming performance at this point is the 256MB. Adding a second card does not double your video memory.

In the SLI category, 9800 GTX is under $200 these days.

You would have to supply a great deal more information about your power supply, before I could say it was ready for SLI.

It has a label on it, or should, that will give all the info.

Evga recommends a 450W PSU with +12 Volt current rating of 30 Amps for a 8800GT KO 512mb SLI setup.
Unless you have a real dog of a budget PSU you should be OK.

If you're using a 1280x1024 resolution monitor the SLI 8800GT 256 might work out ok.

But as Proximon suggests you'll have to look hard at the SLI vs better card upgrade option.