If you already get native boot screen(s) with the Radeon HD 2600 XT -AND- you are adding a second unflashed GPU then you can safely ignore the "will I get a boot screen" question.
I have an Apple OEM ATI [AMD] Radeon HD 5770 connected to an Apple Cinema Display for 'boot screen' features and an AMD Radeon RX 580 (PC version) for powering a 4K display (because the HD5770 won't do it).
I don't know the 3,1 well enough - someone else may be able to confirm that the 5570 (if ever used in older macs) has built in AMD KEXT support and will therefore work once installed in your Mac Pro.