Better a little too much than not enough oil .
It is an OIL pump , not an air pump .
I can see running a bit of oil in the gas if there's an air bubble in the line , as that can act as a flow blockage . But , there shouldn't be an air bubble , if the bleed was done correctly .
I would not try pumping air with an oil pump .
Very likely the exact reason the factory was wise enough to build a bleeder into the pump .