Even Though The Cat Drive Was...

It wasn't until the Regular propulsion was secured and the caterpillar drive was activated that Jonesy did hear singing, which then faded out as they opened range.

This phrase:

I understand contact with the sub may be lost but a bunch of men SINGING in a steel tube wouldn't be heard or couldn't be tracked?

Leads me to think you have a misunderstanding of sonar and how something is detected and tracked.
If they were tracking the singing, then contact isn't lost.
If contact is lost, then they can't hear anything from the sub, singing or otherwise.

PASSIVE SONAR
Is basically, listening to the sounds in the water. You are looking for man made or other unnatural sounds that indicate the presence of a submarine. IF you are detecting these sounds, then you have a contact. When you no longer can detect these sounds then you have lost contact. It does not matter that the sounds are from machinery noises inside the sub, the screws (propellers) churning the water, or Reactor pump flow noise, Or singing.

IF the two subs are extremely close together and the crew on one sub was singing very VERY loudly... Some noise may be picked up by the other sub. As shown in Red October however, is highly unrealistic.

PASSIVE SONAR is also much more difficult to track by even when you do have contact. All Passive sonar gives you is a Bearing to the source of the sound, and signal strength (how loud the sound is). Signal strength alone is not going to give you range to target, though it is an aid to help figure that out. The reason is because a loud signal far away may appear quieter than a quiet signal in very close. It is all relative.

Lets say you pick up the reactor plant noise of another submarine. All you got is a bearing to target. On a chart it would be plotted as a single Line Of Bearing (LOB). You have no idea how far to extend that line, just that the sub lies in that direction. You have no idea how fast he is going or in which direction. You can guesstimate ho far he is not based on the predicted maximum detection range based on the current Figure of Merit (FOM), which is a predicted max detection ranges based and computed from known factors at the time, Weather, Sea Conditions, Temperature and Salinity factors, etc..

In order to turn the contact into a tracked target with a known Bearing, Range, Course, and Speed... YOU have to perform a time consuming and laborious process known as Target Motion Analysis(TMA). TMA is like triangulation where you use two points to find the location of a third... But complicated by the fact your third unknown point is moving, and that you have to provide both base points and that you are also moving. Any change in course or speed by the target can throw your entire solution off and you have to start all over again.

This will give you an idea in the difficulty in using PASSIVE Sonar to track a target...
https://youtu.be/YFlWYLJPX8k


So why use Passive sonar?

1) You can often hear the noise a contact makes much further away than which your ACTIVE SONAR can generate a return echo from a ping.

2) The other sub can most definitely hear your ping long before you can ever get close enough to detect them with the return echo from the ping.

Imagine a police officer with a flashlight trying to spot a burglar dressed in black and hiding out in a huge open field. The Flashlight will only illuminate the burglar enough for the policeman to see him if he is close enough. But the Burglar, can see the policeman by observing the flashlight from all the way across the entire field.

I joined the Navy to see the world, only to discover the world is 2/3 water!

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