That said, you can get leaks. I participated on a research cruise with a French submersible, and there was talk of small leaks with the main hatch seal occurring during descent. The "fix" was to go deeper so the pressure would essentially seal the hatch shut.
I was thinking more like a screw with resistance along the threads such that the pressure goes from 5800 psi to say 20 psi at the last thread or whatever. Then you might get a stable leak.
A screw is there to resist being pulled out. If water got to those screw threads as you posit, that'd basically be like reversing the forces to which that fastener was meant to resist. You go from "big chunk of material to hold in screw" to "little triangular threadforms trying to stay joined to the material around them in spite of 5800 psi trying to transit a pressure gradient insisting otherwise."
I'm not saying it's impossible, I'm just saying if I remotely thought it was possible to end up in that situation, I'd be going back to the drawing board to try to rule out that possibility. My brain just shows me visions of a screw turned into a bullet that barely gets slowed down going through a human body after threadforms crush like tortilla chips, a water cutter blasting through somebody into the opposite ablating a hole and causing a cascaded failure that then shortly thereafter becomes diesel thoomp.
If you'll excuse me, I'm abandoning this train of thought.
But if the leak is noticed at say 20m they would have surfaced.
A leak with the amount of pressure at 1000m would cause a high speed jet like from a water cutter. That in turn would cause the material around the leak to be ground away.
This is really bad for the structural integrity and boom the whole thing implodes in a fraction of a second.
Part of this is the use of carbon fibre, which is a very brittle material. In bike frame failures, for example, carbon fibre doesn't tend to rip a little or bend, it often fractures greatly or even shatters.
Add the enormous pressure difference, and this is why most people assume instant catastrophic failure.