I would guess that it depends on the engine. If you have a dipper type engine and the oil can not flow back to the crank case because the return lines are too small to handle the increased flow you might be in trouble. I would be checking the return flow volume from the valve system. You might have a large amount of oil in the valve system that can not get out. I think the flathead Ford is pretty open below the intake manifold and this would probably not be a problem.
Maybe an expert in lubrication that is AIME, SAE, AGGDE certified or somebody that knows or has a lot of experience with these pumps will respond.
I do not know what the above certifications stand for except SAE. I made the rest up.