The passive sonar from their own prop noise would easily show a mountain. There is a reason about 30 people were demoted due to the incident. Bottom line is they weren’t paying attention to their sonar.
Mountains do not, as a general rule, make noise, and do not show up on passive sonar.
In addition, when running at flank speed the efficiency of passive sonar is greatly degraded by flow and machinery noises.
The way a submarine avoids running into seamounts is a combination of very good maps, very good dead reckoning, (IIRC) gravitational anomaly detection (tied to more great maps), and if all else fails high-frequency (short-range) active sonar. It's a really interesting system! But I don't think passive sonar ties into it.
There's a whole series of highly classified inertial navigation units used in aviation and submarine applications. The ones for use above the ocean's surface have many DoD applications in a theoretical GPS-jammed environment in warfare against an equal-tech adversary.
I've got no idea where jcampbell pulled their information from, but I've never seen anything to even suggest it's possible to use your own prop and machinery noises like that.