John Allen,
The battery does power the PS2 electronics for short periods of time. This runs the sound. A short in the sound subsystem, would account for the battery drain and the engine sounds engaging. The PS2 logic chip reads the energized circuit from the battery and the de-energized circuit from the track as a momentary interruption in track power and plays the appropriate sound set. It may not have been a startup/sequence that I heard, I was in another room when it played. With out a wiring diagram, chip schematic and code documentation, I can not debug this any further.
I am assuming that this is caused by a fault in the sound subsystem in the PS2 boards rather than a physical fault in the wiring. There is no indication of pinched wires nor other wiring defect that would cause a physical short outside of the chips themselves.
All of this is based on my direct observation, I have absolutely no training in MTH PS2 electronics. So I may be completely wrong in my assessment.