Nope, nothing happens. Can't open workshop mode inside quarters. Tried uninstall & install several times, inside and outside the quarters, outside the Prydwen, and then far away on the map. I'll try tomorrow and change load order. But I can see it seems to work fine for everyone so far, so it may be just me doing something wrong.
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None of my characters has ever reached the quest stages needed to "officially" unlock this room, so this didn't go through much testing.
-Are caravans possible: Probably. I don't know how they would behave.
-Compatibility with other prydwen quarter mods: I don't know
As always with settlement mods check if your initial happiness is 50%. If it's 20% it doesn't work properly.
Edit: I did