I know it's not the exact same model, but I've got a Sapphire Nitro Radeon R9 380X 4GB installed in my cMP 4,1>5,1 and it works fine. It doesn't provide boot screens (I get that off my GT120), and it shows up as "AMD R9 xxx 4096 MB" in About This Mac and in System Information, but it certainly does its job well. Playing Civ6 at 4K and getting 60fps – X-Plane 10 renders beautifully etc.
PS: my R9 380X worked equally fine in my cMP 1,1>2,1.