Oil on the pulse side will dampen the pressure pulse and change the response of the diaphragm. I say pressure pulse because it alternates between a positive pressure pulse, piston moving down, and a negative pressure pulse, piston moving up. There are a lot of “depends” here such as how much oil and what engine RPM, but the end result will be reduced pump efficiency. So if its your supply pump you could run out of fuel in the carb or at least go lean, and the opposite if its your return pump assuming a pump-around system. Ideally your pump(s) should be mounted such that any oil can drain out of the pump and flow back to the engine.