You can actually get a GTX 470 to work (even a PC version will work, sans boot screen) with the latest Nvidia drivers. I got it to work, as an experiment.
You will get Resolve to function, but the performance and stability will be close to unacceptable.
I actually got slightly better performance with only the 470 installed. Having 2 cards got worse performance, as illogical as it sounds. Probably due to the bus issues. There can only be 1 16x card running at a time in the Mac Pro 1,1.