Plenty of room under keel.
 

but KLANG BANG BENDING METAL DAMAGE DAMAGE OH MY GOD WHAT HAVE I DONE NOIIISSSSEEE!

Currently trying to sneak up the thames but i've noticed it other times i've been near the bottom hiding.

Is there not mines and nets there.....there should be, :hmmm:

There is an unsolved, long standing bug in the game which means you can't lay on the sea bed. The boat will start grinding on the bottom and taking damage when, if you look on external views, you are many metres clear.

You can also use you depth under keel as a way to tell how deep you are.

Its when you use external cam the it looks like you still have room when you don't.

There is a mod that prevents you taking damage but you are still detectable.

Don't remember the name but it is probably in the downloads section.