Interesting question.
Surely it depends on the size of the ship & the depth at which it lies. Whilst a well costructed 9hull will float on the surface because of its displacement (taking into account its average density, including the air it holds) once it has sunk, the same amount of air may be insufficient to raise it. Air gives a good lift in water because of the relative densities, but at depth the air will be compressed by a much greater factor than the water, thus bringing the relative densities of Ship+Air and Water much closer.
Free divers (a sport in the news recently) know that there is a depth at which the natural positive bouyancy of a human body becomes a negative quantity.

Nigel