It is one thing to use such techniques to test something in a quiet area like a testing chamber, and something completely different to use this technique not only in a rocket that is accelerating at 32 m/s^2 but also has a whole bunch of other noise going on from nine operating turbo pumps, the rocket engines themselves, and other things rattling around tied to that whole system. In addition, to be able to locate a cause while the whole rocket is undergoing massive unplanned disassembly (aka an explosion releasing as much energy as a small nuclear bomb). Also doing that remotely off of recordings made on less than ideal microphones sharing bandwidth with many other more critical data functions over 30 miles away from where you are at.
As something SpaceX can and perhaps should be doing as a part of their Q/A analysis, no doubt using some sort of sound probing to detect faults is going to be done. I just don't know if this has been done on something like a black box of an airliner to perform fault analysis post-mortem on a vehicle failure.