It should pick up fuel as the pump should self prime, but you need to put enough in to make sure the inlet us under the fuel level.
If it doesn't self prime or develops an airlock it is recovery and to the garage as the fuel has to be pulled through from the engine end....and on our diesel it then has to be bled of air.
On Aldermog I'm not brave enough to find out.
It should be no problem to run out of fuel in the Morgan. The pump is self priming and will pressurise the fuel rail that feeds the injectors without any problems.
Modern diesel engines with common rail should not present a problem as they will pressure up in the same way. Only the old diesel injectors with a mechanical pump that had fuel lines to each injector needed bleeding. I know because I had to do it more than once on farm vehicles in my yoof.
I managed to run out of fuel in the Alfa the other day and just managed to coast up to the pump. After filling with diesel I had to crank the motor for about 15 seconds before it started. I had an engine warning that turned out to be low fuel rail pressure and I cancelled that when I got home using my OBD2 reader (Torque on my Android phone). No problems resulting from the experience but I now know that when the needle is on empty on the Alfa it really means it.