I think that it should be enough power.
Guru3D got their test system with one 5970 in it to pull almost 450W from the wall outlet which would come out to be about 382W being pulled from the PSU if the PSU's efficiency were 85%.
Here's how they did it, and it includes more information about their test setup:
The methodology is simple: We have a device constantly monitoring the power draw from the PC. After we have run all our tests and benchmarks we look at the recorded maximum peak; and that's the bulls-eye you need to observe as the power peak is extremely important. Bear in mind that you are not looking at the power consumption of the graphics card, but the consumption of the entire PC drawn and measured at the wall socket side.
Our test system is a power hungry Core i7 965 / X58 based and overclocked to 3.75 GHz. Next to that we have energy saving functions disabled for this motherboard and processor (to ensure consistent benchmark results).
Our motherboard also allows adding power phases for stability, which we enabled as well. I'd say on average we are using roughly 50 to 100 Watts more than a standard PC due to these settings and then add our CPU overclock, water-cooling, additional cold cathode lights etc.
Keep that in mind. Our normal system power consumption is much higher than your average system.
Even if I add 200W to this, that would still only be about 550W being pulled from the PSU. I mean, 450W + 200W multiplied by .85 for 85% PSU efficiency results in a little more than 550W (exactly 552.5W for this calculation).