Unless they are modulating or encoding the ping in some way specific to that car, yeah, it will work.
Decades ago a buddy picked up an old 10 GHz klystron-powered traffic radar. He built an audio modulator for it, impressed on the klystron's power supply, and by varying the frequency of the audio generator he could dial in any speed on the radar's speed display (mechanical needles at that time). Why? The AM modulation simulated the doppler shift that the traffic radars worked on. He figured out that if he got the AM modulation up to very close to 100% it would affect the cop's traffic radar (he could dial in any speed on their display because his transmitted signal was far more powerful than the reflection from their own radar transmitter).
Yes, we had some interesting drives in those days. Moving precisely at the speed limit, the Fuzz Buster goes off and once the cop has you clearly in view because no one else is near you, flip the switch to 125 MPH and watch their reaction all while staring straight ahead down the road to avoid them seeing you watching them.
Those things had an audio output so the cop could hear the doppler frequency so they knew it wasn't just an errant needle.