Nop... consider.
2x CPUs 130W rated. So thats 260W, right there. However, no CPU consumes the rated, so it's give or take ~260W.
Each 5770 is ~108W, given two, that's ~216 W. Right off the bat we have ~476 W being consumed. Not bad; however let's look at the side where its not a dual 5770 setup.
The PSU on the Mac Pro is rated for 980 W of power, but for simplicity sake let's say 1 kW. Now, factor in the Super drive, Ethernet, Airport, at least 1 HDD and peripheral docks/cards you are looking at ~100 W. Take into account a 20 W per 1GB of memory (assume 6GB) and you've got ~120 W more. So far ~ 220 W more.
Now we have ~480 W [~260W + ~220W]consumption leaving only ~520 W left for a GPU. Currently, the HD 6970 requires 2x 8-pin connectors to provide 150 W per pin. That's 300W right off. So we are left with ~220 W in the system. Now, factor in that PCIe slot power draw at 75 W and we've got a ~145 W left over. ~145 W is cutting it too close and something will yield (yes I do realize 145 W is a lot more, but read on). Now, the sad part, we were assuming 1kW PSU which is not the case; it's 980 W meaning there will be less power, ~125 W. Now, also take into consideration no PSU is 100% efficient, hence there will be greater power outlet draw and the PSU will be operating at high voltage/amps and its life span will decrease dramatically over very high usage.
In other words the current PSU may come up short. Add to that the fact that all current shipping and past model Mac Pros don't have extra dual 8-pin connectors. They have dual 6-pins. There is an adapter to make a 6-pin into an 8-pin, but it is risky at best, big no-no.
So as you can see an HD 6970 would be barely supported on current models. Future models? Perhaps yes assuming Apple bumps to 1.1kW or 1.2kW PSU.
Take into account this was calculated assuming 6GB of memory and 1 HDD, anymore RAM (20 W/1GB) or HDDs (10W/disc) and the consumption will go up. Also, assuming nothing is hooked up to peripheral ports; like a small external drive that draws 5-10 W.