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On the older Vane Airflow Meters, yes but you would get a start, run, stall symptom. (Fuel pump cut off switch was internal to the VAF).
Can't recall ever seeing one cause a no start.
I've seen this on a Pathfinder, where a bug had jammed itself into the sensor. It had injector pulse, but the pulse width was so short that the engine only coughed and sputtered occasionally during cranking.
Yep had the same on a Jaguar S Type, would start but immediately cut out
Started and ran ok with MAF disconnected, found what looked like wasp jammed in the sensor