It depends on the particular card in question.
In the case of adding a DVI port to a RX480, the original design of the 480 already has the circuitry in place for a DVI connector, and the connector itself is simply missing. You can actually see the solder pads where the connector would be attached on the PCB. This type of scenario is typical, where Nvidia/AMD will build in the potential for many more ports than are actually used on the reference cards.
That said, there are cases where AIB manufacturers go well beyond what was ever intended, and in those cases they often do need to create their own circuitry for their custom cards.Edited by Zero4549 - 9/16/16 at 1:35pm