What is involved in converting a PC video card to have boot screen on the Mac?
From what I understand, it's not the Mac Pro, it's the graphics card that needs to be flashed so that it's "Apple approved"

For example, on MacUpgrades, they list an Saphire Radeon RX 580
with 8GB RAM


  It has been flashed to work on the Mac Pro 2008 (MacPro 3,1) - Mac Pro
  2012 (MacPro5,1) models.


I ran across a video of the flashing procedure for a newer (but same family) of video cards - though the procedure does require the use of Windows (meaning Bootcamp).

You will need:


GPU-Z to back up your cards firmware
ATIWinFlash to flash the firmware
The EXACT firmware for your Mac and video card


I currently don't have the required components to test/verify this procedure so proceed with caution.  If this is something you are not used to doing, definitely seek out someone who can assist you with this as you run the risk of bricking your GPU.