Can I use Clover on a real Mac Pro for device spoofing an unsupported AMD GPU?
I think you are going about this the wrong way. I think turning your Mac Pro into a hackintosh will create far more problems than it will solve. Updates will be difficult, and clover is a pain to work with. There is a reason hackintoshes are specifically NOT recommended for people who rely on their computers to do important things (such as work).

There is a way to get the GPU to work without going through this complicated mess.

First, do you need to see your boot screen on every boot? If so, this becomes more complicated. You'll probably want to jump on the Nvidia train and get a flashed card (the only ones I know of are sold by MacVidCards). The only other option would be to use the new card in tandem with the old one, and have a monitor for the boot screen plugged into the old card. If you don't care about the boot screen most of the time, keep your original card handy, because you will want to be able to access it every now and then (for recovery mode, etc).

Now assuming you don't need to see the boot screen, you do need the GPU to work. Because you have an AMD GPU, not Nvidia, the drivers are built-in to MacOS. This means that if right now you removed the old GPU you have and put the new GPU in, once you get through the boot sequence, you should see the screen fine.

Please let me know if any of this was confusing or did not work.