Another FYI. The fuel pump sits in fuel. There is no way for it to go dry so priming is not what is happening when it makes noise. It has to get the fuel pressure up to 43psi. Then the pressure regulator valve opens to divert some fuel back into the tank so the pressure in the output pipe stays at 43psi. When that happens, the pump gets quieter.
As long as the pump has enough power to reach that 43psi, the engine can be bump started.