RTD did state back in 2006 or so in a response to a question about is there a Doctor in Pete's world that the Time Lords are unique to Doctor Who's "Prime Universe" and as such neither they or the Doctor exist in other realities. And it seems Moffat and Chibnall have adhered to that in their runs as well.Very few, which is a shame. We had Inferno in the Jon Pertwee era and the 'Pete's World' storyline in Tennant's era, but it's astonishing how they haven't based a whole season on the possibilities of other universes.
Who wouldn't want to see an evil version of the Doctor from a parallel universe, played by a past Doctor? Or a good version of The Master? Or kind Daleks?
The Division were all but presented as an organisation that existed in the void between universes, so it feels like they missed an opportunity there.
Tie-ins have taken a slightly different perspective on the matter. IIRC, novels from way back in the day have stated the Dictator in the alternate universe in Inferno is that universe's Doctor. While the Matt Smith era novel Coming of the Terraphiles stated that during the Time War, the Time Lords drafted their counterparts from across the multiverse, and thus when the Doctor killed wiped out the Time Lords at the end of the war, he annihilated all the Time Lords across the multiverse. Though that probably isn't compatible with how Day of the Doctor would later depict things.
Of course, with RTD back in charge, he's likely going to stick with what he said in 2006 anyway.