It's always good to have a clear inline fuel filter upstream from your fuel pump to see if there's fuel in the line.
If the fuel pump is priming and pumping gas to the carb, there is no reason the carb shouldn't be priming. Only possibility is sometimes the fuel inlet needle can swell up (especially from junk ethanol gas) and stick in the inlet and not let fuel into the float bowl.
Have you tried taking the fuel line off the carb and into a jug and turn the key on to see if fuel is pumping?