You can't build other races' stuff if you steal a constructor frigate or starbase builders
And yeah, the Subverter default ability is pretty useless to Advent, since it's mostly designed for phase missile bypass. Hoshiko I'm pretty sure is set up that it actually needs the research prereq for the ability also, not just the ship hull, but even if not the Advent have their own repairer so it's nothing unique, though Hoshiko is a bit better at it.
So as far as support ships, Cielos and Overseers are the only ones you can get decent use out of it. Other than that, carriers and heavy cruisers are obvious choices since they're powerful and expensive.
If you're playing Entrenchment, grabbing a bunch of Ogrovs from a TEC is also pretty good.