A few thoughts/responses:
-Yes, it IS possible for a mechanical pump to be installed correctly & still not deliver any fuel. Causes could be "ruptured diaphragm" (never a phrase that any guy wants to ever hear!)

, broken drive arm, or even a drive arm that simply "hangs-up" (I had this happen on a Ford 351 Cleveland w a cheap aftermarket mech pump installed...). Could also be a complete loss of prime.
-On my Austin FX3 London Taxi the mechanical pump has a built in prime lever. This particular FX3 has the Austin 2.2L diesel installed in it, and diesels are PARTICULARLY unhappy if they lose prime! So evidently Austin decided that it was worth it to install a prime lever.

I wonder if this same pump would fit a BugEye??? HMMMmmm... might need to do some measuring.....
-Elect pump installed between the tank & mech pump seems like a good modern day solution. Besides, they are so low cost that it is also the more economical solution!!
-Looking back to the days of Model-Ts (I have 2 of these wonderfully simple machines...) it is worth noting that Model-Ts didn't even have a fuel pump! (nor a water pump, nor brakes at the wheels, nor turn signals, nor brake lights, nor shock absorbers, nor a gas pedal, nor a starter motor, nor an oil dip stick, nor.... but that's a whole 'nother discussion...) They used a gravity feed system that took advantage of the height difference between the fuel tank (located under the driver's seat) and the updraft carb (located on the lower RH side of the engine). UNFORTUNATELY this system didn't work very well when attempting to climb steep hills!! Typical solution for this problem was to BACK UP the hill!! (many roads even had a turn-out area specifically designed to facilitate this change in vehicle direction.) BUT some clever T-owners adapted a tire valve to their gas tank cap & pressurized the system using their tire pump (a standard piece of equipment for a T)! :banana:
-I've seen a Spridget owner who followed this same line of thought by adapting a fuel cap to have an air fitting on it. He would simply connect the fitting to his compressor (at low pressure) and "whola" the fuel system was primed!! :thumbsup:
That's my 1.5 cents worth!! (the dollar isn't worth what it used to be.....)
-Bear-