If the air has nowhere to escape to, then yeah it will be there. The thing is, depending on how deep it is, it is going to be at a higher and higher pressure than at sea level. The water pressure will try to push into the space, compressing the air until the pressures between the two are equal. That’s why in the movie Sphere, they have to breathe a high-pressure gas mix that is mostly helium, because of how deep they were, having the air pressure very high inside the habitat made it a lot safer from rupture.
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