No. That piston needs to move. When you start revving the engine higher, vaccum drops and gravity takes over letting that piston travel downward, which gives it a shot of fuel to compensate for the need of more power.
As mentioned above, I used vinegar to soak that portion of the carb overnight which dissolved most of the rust and gunk in the passage, letting the piston move slightly. Give that a go and try carbkings method with the grease.
Jeff