If CPS goes faulty the engine would stop because BCM uses the signal from it to determine the timing when should turn on the injectors.
It should (but not sure) bring up a Check engine light and it should have a fault code stored considering it as a major malfunction .
One way to find out (quite hard - being above the bell housing ) is to unplug it from the harness and see if brings up a light or fault code .
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