How can the DD hear anything when they have no detectors to pick that up? They do not hear that stuff on the Hydrophones, it is not modelled in the game.
I ping for depth right next to a DD and they never do anything. I hit them with active sonar to range and they just sit there.
I think they should be react with chance to hear you doing it, but the game engine does not in my experience pick up any sound from your subs depth under keel, or acitve sonar range pings to target.