Hi Dave,
The fuel is not supplied to your generator via the engine fuel pump. The generator has a fuel pump mounted on it with a suction line that runs into the fuel tank. The three ports on the engine fuel pump are for feed, return and evaporative emissions. Generally if your fuel tank is at 1/4 tank or lower your generator will not pick up the fuel as they don't want you to run the fuel tank dry by generator usage. The best way to diagnose if the fuel pump is your engine performance issue would be to hook up a fuel pressure gauge at the fuel rail on the side of the engine. I would contact your generator manufacturer to inquire about the fuel feed and fuel pump system for it.