From being one that has deadened my doors and heard a before and after I have to say yes sound deadening helps a ton! From what I know of home and car audio here goes my figures....
Deadening doors adds wieght to the metal surfaces which reduces vibration. While doing this, it does not allow the surface the speaker is mounted on to move as much so the speaker cone moves as it should. Second it does not allow for the metal to move as much, making the enclosure less likely to expand. The same reason we put braces in MDF made enclosures. Third it helps seal the door more then stock, so air is not able to escape through as many holes, making you door a more efficient enclosure.
I get this reasoning from home audio where people spend money on spikes to make sure there home speakers do not move when playing, and they put rubber feet on components to reduce vibration, both of with impede perfect sound reproduction.