From my 12 years on this forum, I'd say no. MANY CPSs have failed, none caused that, what they cause is the engine to quit.
Keep in mind, the ECU still knows where the cam is, as there is a sensor on that as well, so it's not like the loss of the CPS signal means the ECU is going to fire plugs randomly.

In fact, if the sensor fails enough for the ECU to light the CEL, it will also stop firing plugs (and, I assume stop firing the injectors).