I've never seen the AI use a space yard ship to repair other ships, even though it builds them. I think this is another area where the AI is not "finished" yet.
Nope, I saw an Ork shipyard, repairing the damaged engines of one ship.
The bad thing, was that I saw a Pyrochette shipyard, building a defensive base into the space! This was when I decided to don't build shipyards anymore!
I think that's more useful, make ship designs with Repair Bays.