No? It's the hull of the vessel that counters the outside pressure. The main reason to use a submarine, instead of scuba diving, is to shield yourself from the pressure. If the inside pressure was even close the the outside, which it would have to be to keep it from imploding, you wouldn't need the submarine at all; you'd be crushed regardless.
At the depth of the Titanic, roughly 4000 m, the water pressure is ~400 bar. The record for highest survived air pressure is around 70 bar. That was for 2 hours, breathing a special gas mixture of 99,5% hydrogen and 0,5% oxygen.
I find it highly unlikely that they'd rely on the inside air pressure for anything other than the comfort of the passengers.