To answer the question definitively, yes, U.S. submarines still use the old-fashioned type of diving alarm. It’s a very loud, distinctive AH-OOGAH type of alarm. (Actually, I’ll note that my knowledge goes back 10 years ago to the improved Los Angeles-class submarine I was on.)
The standard order I used to give when standing watch as Diving Officer of the Watch (DOOW) was, “Chief of the Watch, sound two blasts of the diving alarm. Announce, “Dive, dive!” Sound two blasts of the diving alarm.” The next order was, “Chief of the Watch, open all main ballast tank vents.”
(Later, as a qualified Officer of the Deck (OOD), I simply gave the order, “Diving Officer of the Watch, dive the ship. Make your depth 150 feet.”)
Anyway, a loud distinctive alarm is no big deal, because a 6,000 ton submarine on the surface is not exactly stealthy. Also, you don’t want it to be a surprise, if, God forbid, a hatch was still open–very unlikely, since this would be clearly evident on the dive board indicators in the control room.
In addition, there’s a big difference between “air noises” and “hull noises.” You can scream as loud as you want on a sub, and there are many loud alarms and announcing systems on a sub. None of these “air noises” are a particular concern during normal “patrol quiet” conditions. Dropping a wrench into the bilge (where it directly hits the hull) is a very different matter. This noise could travel for miles.
(However, during “ultra quiet” conditions, we did in fact secure all unnecessary noises, including the announcing systems. A person in all spaces was required to be on the sound-powered phone system. It was mostly psychological, to prevent personnel from doing things that might transmit noise through the hull.)