It doesn't work like that.
The easystart simply provides the fuel to run the engine for a few seconds.
However if the EDC doesn't get a timing signal from the cam position sensor, it can't know which cylinder to inject fuel, being a sequential injection system.
So as the EDC doesn't know the injection sequence, the engine would simply stop running, after the easystart was burnt up.
In normal conditions, the EDC references the pulses received from cam and crank position sensor, which allows it to identify the firing sequence, initiate injection and start the engine.
Once started, the cam position sensor is no longer needed, as the EDC now knows the sequential timing, so will continue run the engine using the crank position sensor as the timing reference.
It's only after the engine stops, that the timing reference is lost, so the cam position sensor is required again, for the restart.
