It would have to completely choke off the intake for it to starve the motor for air. I don’t see that being possible considering most factory, unmodified cars have an air box with a filter panel that would be too large for a stuffed up paper towel to affect. It could definitely obstruct airflow but I highly doubt it would choke it off completely.

There is still air inside the motor when it’s shut off so it should at least fire a few times before getting choked out/starved for air.