Since the ECM is removed, the pump will not run with key on - it will only run when starter is engaged long enough for oil pressure to be read at the oil pressure sending unit, whicg powers the pump after the ECM has been removed. There also will be jno priming - which is fine - with a carb, you have plenty of fuel stored in the bowls to start the car, so you don't need priming, nor do you need the pump to run before oil pressure is built up.
Even if the pump ran with the key on, it wouldn't 'fill' the carb - that's the whole point in the return-style regulator (mallory 4309) - the excess fuel is returned to the tank through the regulator and the return fuel line.
So - everything will work fine. The only issue is if the car sits unstarted for like 3 weeks, the fuel in the carb bowls can evaporate after time, and so it takes a few cranks to build up enough oil pressure to run the fuel pump to get the bowls refilled - but that's the only time.
You can do like I did, and remove the two larger wires from the 3 wire connector on the oil pressure sending unit, and connect those into a relay with a ground and a hot-in-run wire, so that when the key is turned on, the hot-in-run wire will energize the relay, sending power to the fuel pump, and thus running the fuel pump whenever the key is on - but it's not necessary. The only reason I did it, was that when the oil pressure sending unit goes bad, the fuel pump won't run - this left me stranded for 15 minutes once, but the quick fix was to just unplug the oil pressure sending unit connector and jump the two larger wires in the connector with a paperclip to get me home until I got a new oil pressure sending unit installed.
This new relay setup also allowed me to mount a switch in the cabin that makes the ground contact for the relay - so that now unles I flip the hidden switch, my fuel pump will not run at all - added theft security!
That makr sense, or did I ramble too much?