>>> my question is does the ecm have to receive a signal from crank angle sensor to initiate the fuel pressure regulator solenoid which controls the fuel pressure in fuel rail.<<<

The PWM control for the DRV will be dependent on engine speed and engine load, referenced to a look up table inside the ECU, with the FPS completing the closed loop control circuit.

I would expect the DRV to be fed with a set PWM signal until the FPS signal is matched to the current engine speed/load map.

Then the PWM will move with the engine speed/load demand placed on it.

As others have said, scope the DRV with the Ignition on and the engine not running to confirm.

If the crank sensor was at fault I would expect a fault code because the ECU should "see" the cam signal without the crank and log a code somewhere around the P0335 range of codes.

If the rail pressure is very low when it cuts out perhaps you need to sit down and work out everything that could cause that. HTH

Regards Mark