Ok, carbs 101.
There's a reason why you set the float to a particular height. It's so the right fuel pressure 'head' is applied to the ports (idle and progression) and the main discharge in the venturi. Set the level too high and your engine will run rich, too low and it'll run lean. Without the fuel pump refilling the fuel bowl/float chamber, the level in the fuel bowl drops, and that causes the mixture to lean out. It will continue leaning out until the engine can't fire it, at which point the engine will stop, despite there being fuel left in the carb. It's just not enough to produce a strong enough mixture to fire and sustain the engine. Now, the accelerator pump fuel well sits slightly lower than the bottom of the float chamber, so any fuel left in the chamber will collect in the acc. pump well. That's why, when you pump the throttle (and activate the acc. pump) the engine gets a couple of shots of fuel, and that's enough for it to run for a few seconds. But it's only running on the fuel shot into the intake by the acc. pump, it's not drawing any of the remaining fuel in the float chamber, because it can't (the fuel level is way too low).
Chris.........