By the time any significant amount of air makes it's way in there, I'd think that the engine would stop running. That is to say that the volume of most pumps can not bring the system with air in it to a significantly high pressure.
A pressure washer pump, which uses plungers, pistons, whatever, when it sucks up some air the pressure is gone forever it seems. 2600 psi to a trickle in 1 second flat.
A mechanical injection pump, with the air in there, won't pop open mechanical fuel injectors. There's no longer enough pressure.
Similarly, the design of some modern high pressure diesel pumps uses pistons/ plungers. Once air gets there, with it's compressability, if you will, the pressure created inside the pump would be insufficient for it to flow into the high pressure side of the fuel system.
To add to that, if there's check valves it won't go to the high pressure side. The air expands on the intake stroke and then limits the amount of fuel that can be brought into the chamber of the pump.
I've had the unfortunate experience of refuelling my diesel on the side of the highway after running out. I had to go so far as to crack the lines to the injectors to get the air out of there. Even after the lift pump did it's job the high pressure pump could not with the air behind it.
Engineering student. Electrical or mechanical, I can't decide!
Minoring in psychology