A worn, weak fuel pump will not hold a prime to the cauburetor if the check valves are bad. After the engine is shut off the fuel in the fuel line (and filter if installed) which is under pressure will slowly leak back through the pumps internal guts. The only fuel READILY available would be what is stored within the float bowl.
A fuel pump is tested with the ignition OFF during cranking, using a remote stater switch and fuel pump tester. If the pump is weak, it will show up during this test. The internal pump parts are moving at their slowest during cranking, if the pump cannot supply ample fuel pressure and volume during cranking, it absolutely cannot during high fuel demands such as high speed or when the engine is under a heavy load. My bet is, that this pump will not pass the test.
And OH by the way, FYI, the accelerator pump IS NOT supposed to have to be used to supply fuel during start up. The accelerator pump (plunger/spring/check ball/nozzle etc) are components of the ACCELERATOR circuit which is incorporated into the carburetor to minimize lean mixture conditions when the throttle valve is opened suddenly.
Last edited by WillsLimo; 11/26/2007 1:06 AM. Reason: addition