Gob is obviously connected to Carol, (Carol's Place in Underworld). Does he ever leave Moriarty's Saloon in Megaton...?

Hmmm, no I don't think that he does. From what I remember, he left Underworld to seek a new life in the Wasteland but got captured by raiders until he was rescued by Moriarty.

Now he spends every day behind the bar in Moriarty's Saloon. It would be cool to have a mini quest attached to him in some way, I always liked Gob.

Actually Moriarity bought him as a slave. He won't leave the Saloon, but if Moriarity "leaves" Gob and Nova take over the place. I like Gob too, but I doubt he is hard enough to be a good (combat capable) companion.

It's too bad, I would have appreciated being able to reunite Gob and Carol.