But also no, if it’s capsized, the boat may right itself in time before it floods to a point where it sinks.

A fully submerged boat will not bob to the surface. The keel adds stability and (counter)weight, but negative buoyancy - what keeps the boat afloat is the air in the hull.

Once it’s fully submerged, there’s nothing pulling it up (unless you have some seriously good (and closed!) hatches…