The Carter will prime, but not all the time if it has to pull the fuel out of the tank. I ran the tank out of gas last week. I added gas and switched on the ignition. After waiting a minute or so for it to self prime, I started to worry about damaging the pump and switched off. I used an outboard motor style squeeze bulb to fill the intake pipe and it's worked fine since then; starts pumping right away.
Again, this would be an issue for the later trucks where the fuel has to be pulled out of the tank. Gravity feed from the bottom of the tank to the pump inlet would be just fine.