No, the leak jet
controls the size of a second opening in the accelerator pump circuit. Picture a pipe running from the pump at the bottom of the carb straight up to the throat, with a hole in it about 2/3 of the way up. The hole is the leak jet.
The reason it's used is that you only want fuel to squirt from the pump when the throttle is opened quickly, not when you're just cruising along and you only open the throttle a little, or slowly. Too much gas then would cause a stumble. By putting the leak jet in the circuit, opening the throttle slowly pumps gas only as far as the leak jet, where it spills back into the float bowl.
Opening faster builds up enough pressure for it to shoot out of both places. Changing the size of the leak jet allows us to control the effect to get the right sized shot of fuel when we we want it.