Electric fuel pump on carb motor

I have twin 5.7/350 carbs, mechanical pumps. I replaced both pumps in 2016 and overhauled the carbs. If the boat sits particularly after running o while (hot) carbs will tend to boil off the gas and the bowls will be low or dry after a few days. They will need to be cranked a good 30 seconds to refill, then pause, pump once and then they will usually start right up.

Carbs will never start as easy as your MPI after sitting, just one of the advantages of fuel injection.
Before assuming a pump issue check the carbs over (especially if it runs well after starting and at WOT)
Yes, you need the choke to be working properly. Remove the flame arrestor, be sure its clean. Cold check that the choke sets properly with one pump of the throttle. If not fix that first. When you pump the throttle be sure you get a nice spray of fuel if not the bowl could be dry or the accelerator pump could be worn out. Crank it a bit to be sure the bowl fills up and try pump again.

The electric pumps for carbs are not usually finicky. They should be specifically for carbs, low pressure 5-6 psi only no more.
Now it may depend how the previous owner wired it. If straight to the ignition it should cycle with the key. But unlike a car or MPI where the computer controls it, it may run continuously. If a relay or oil pressure switch is in line it may only pump when the engine has oil pressure and/or when actually cranking. In a boat this is the preferred safest configuration. So it will not keep pumping if the engine fails to start or if it shuts down for any reason even if the key is left on.

 

Does the fuel pump run when you turn the key on without cranking the engine. There should be a relay that would run the pump for a few seconds. That may be bad.