Even if he was underboss in name, he never had the official underboss authority. As the the series moved forward, Tony looked at Paulie like he was a joke; an ill tempered baby with moderate earning capabilities. If you watched the show you know that Tony's number 2 was Sil. As previously stated, Chris at one time could be viewed possibly as a number 2/3 type candidate. Even in the last season, Chris accompanied Tony to that meeting about asbestos removal with Phillie and crazy eyes.
I no point in the series, whether having the underboss title or not, did Paulie have any more power than that of a capo. I don't recall once when he was treated by Tony or the family at large as anything more than a Captain.