I am concerned about the potential port mapping issue. My Gigabyte RX 580 Gaming 4G has 1 DVI, 1 HDMI and 3 DP ports while the Sapphire Pulse has respectively 1, 2 and 2 respectively, AFAIK.
My HP 30" screen requires a dual link DVI connection - it has no other type of ports.
And is there any other side-effect resulting from pretending a 4GB card is a 8GB one?
Change the part number is not pretending a 8GB card in this case. Just make the OS give it a correct ident and apply the correct framebuffer. The driver won't try to access any VRAM is not there.
HOWEVER, in your case, the framebuffer will be WRONG. So, one or more port may not work properly after you flash the card. Since there is only one connection available to your monitor. If you are unlucky enough to get the DVI port fail after the flash. You may not able to see anything on the screen in MacOS.
But screen sharing should still working. Therefore, you better setup a screen sharing first (in not yet done). If you have another Mac, that's easy. If not, Chrome Remote Desktop can do the job properly for free with almost any other device (including smart phone).
So, if your card can't display anything in MacOS after flashing with the "new" part number. No panic. Use remote control to get yourself back into Windows (I expect you have Windows, otherwise, how to flash the card?). And since Windows can properly identify your card and apply the correct framebuffer. You RX580's DVI port will work properly at there, and you can flash the original ROM back in.
N.B. even though both your card and the PULSE has only 1 DVI port, the DVI port can still fail if apply the wrong framebuffer. Also, I assume you only change the part number but not anything else. Otherwise, if you accidentally kill the card by flashing a bad ROM onto it. It can be pretty hard to recover.