Could the Quake engine support Portal- or Build-engine-style world portals? Would such a thing be possible with QC? Are there any mods that add them? Thinking on the level of pure BSP geometry, it must be possible somehow.
I don’t think it would be possible in QC, but I think it is possible. That said, you would have to modify the engine itself along with potentially creating your own extension to the BSP format as well as modifying a BSP compiler.
Despite the challenge, I would love to see that in the quake engine. It could open up a lot of possibilities, many of which would fit the Lovecraftian theme of Quake. It would be awesome to see maps sorta like Impossible: A New Reality: https://www.youtube.com/watch?v=YtLoHSIKp5Y
There are multiple portal gun mods that use Quake teleporter functions.
FTEQW and Darkplaces also support actual portals (in DP called warp zones). Try http://triptohell.info/moodles/junk/pourtall.pk3 with a recent FTEQW. You have three weapons that look the same. Two are the portal modes, the other you can press and hold to grab and move monsters.
Darkplaces warpzones seem like a good bet, but there’s zero documentation. I know they exist in Xonotic, but I have no clue if that’s one of their team’s features or one of LordHavok’s.