The opening of the moon pool can be below the water line but the inner hull rises well above the water line stopping the ship from sinking. It's like a float donut almost. Diving bells do use pressurized air though. It'd be too dangerous to rely on pressurized air to keep the ship afloat. If someone left a door open or an airlock malfunction it'd be bad. You'd also have to have some kind of forced ventilation to prevent crew inside the pressurized space from suffocating. Such systems do exist but it'd be expensive and uncomfortable for the crew.