Not a chance. The whole problem with subs is that water weighs about 8lb per gallon.

So, at 4000m you're looking at something between 4500 5500 psi. Thats a small truck worth of pressure every square inch in the hull. Once you breach the structure, think crushing a tin can in the middle, things collapse pretty fast.

As do bodies. If you figure your body is 2 foot by 6 foot, the pressure would be like parking 100 fully loaded 18 wheelers on a single body within a split second of each other.

Every book or encounter you read about submariners has a section talking about the creaking of the bulkheads and wondering how long it can hold because it's such a nature defying act to build something that can hold that pressure out in the first place.