I had 10.9 Tiamo's running on my macpro1,1 with a 5770 GPU. I installed the pre-cooked Yosemite and upgrade to 10.11.1. With 5770 it didn't work at all, and with the old 8800GT it booted, but sluggish gfx until it had a GE panic.
Picked up a windows HD7950 and had some hassles sorting out the 2X PCI-Express 6 pin power, but it did boot 10.11.1.
I used the Apple store to upgrade to 10.11.3 and found it no longer worked, and can't see why since I have no boot video output. I replaced the boot.efi in both places without success. Eventually also replaced the recovery boot's boot.efi as well, and it come up with "finishing installation".
At the end, I now have 10.11.3, with HD7950, on a MacPro1,1. There is no boot time gfx still, and I can live with that as long as nothing breaks, ever
I guess I should see how much work it is to flash it. (If you can only flash from windows, I don't think I can be bothered )