Not on the waterfall. This might be used to listen, but is not used in the firing solution.

I'll chime in here as the older guy and used the older systems.

BQQ-5B had two analog broadband trackers. Tracker Alpha and tracker Bravo. They each had an exact mechanical representation of the sphere (they were about 2.5ft diam), called a Compensator. The sonar operators had to clean these two compensators each day. The Q5B also had two digital (non-compensated) trackers, Tracker Charley and tracker Delta.

The beamformer would scan the entire sphere for incoming energy in under 1 second, (I know the actual time.....), and display the result on the display.

You also have an audio cursor, which allows the operator to listen to what ever they want to. This is that sonar by trackball that was mentioned.
An average or better broadband operator can just listen to a contact and give you a good id... merchant, trawler, warship, submarine. Sometimes in seconds. There are other things they can do aurally but I will not get into that here.

A good Fire Control Coordinator (The XO) will take the Sonar solution and compare it to the generated solution in Fire Control. Since the CO, XO and Fire Control operators are always doing mental TMA in our heads, the FCC uses this as another input to prove, disprove or refine the Fire Control solution. This data is not wasted or a waist of time.

Depth from the Maritime Patrol Perspective...
 

Ex P-3C Pilot type here, but I spent a lot of time in the Sensor 1 and Sensor 2 locations onboard, learning. I know we were able to determine depth somewhat easily using a series of gram visible striations, typically generated on the waterfalls due to interference patterns between narrow band frequencies. That said, the science has been discussed here, and with the bending of sound due to SVP, you had to have the INSITU information well understood using BT buoy data to make it work. A good SS1 could determine depth fairly well given the right information I think. I suspect the same physics works from a submerged vantage point, since our buoys were "submerged" after all...