The Thresher nor the Scorpion had a “conning tower”. The old diesel boats had conning towers which were shaped like a rounded off barrel as part of the pressure hull but outside of the actual full pressure hull inside the sail. Those two classes of nukes did away with the conning tower. You may be referring to the “Sail”. Whether or not knocking the sail off would make it sink is questionable. A catastrophic event like that would probably make it sink but that is not absolute.
true, as i mentioned, it was a rumor.