I really doubt this, but I'd love to hear from a maritime expert.
No expert needed: it's simple physic matter!
If anything sank, it will be less and less buoyant with the pressure increasing. Even if the cabin sank in a whole, and it opened when it crashed on seabed, I don't see anything could be buoyant at ~5000 meters: all things which might float at the sea surface are crushed by the pressure (more than 7000 psi!). Polyethylene and like have an intrinsic density > 1: porous materials with "opened bubbles" are water impregnated and those with "closed bubbles" are crunched beyond floatting possibility. Even organic things which will slowly rot (sorry for the picture...) can't become buoyant with carbon dioxide or methane gassing: CO2 is solvable in water (and if protected from water, CO2 is a liquid at this pressure), and CH4 gives hydrate.
So...