My K-Jet doesn't prime before starting either, its done that for the past 18 months. It will only need to prime if the fuel pressure is low. On a failed start, you hear the pump prime.
In terms of the pump, just because its drawing a +12v and whirring doesn't mean its working! My old fuel pump used to make all the right noises, but it didn't actually do anything. Best way to find out is to remove the fuel line off the fuel dist block on top of the air filter and see if theres any pressure, or remove the pump housing altogether and test the lift pump on its own, and check the pressure pump on its own.