Sorry to come across as doctrinaire and preachy, but I really believe the old wisdom that all bilge pumps should have separate hose and thruhull systems; i.e. continuous from the strum box to the transom exit fitting. Never should pickups be "combined" and any hose over about 20 years old should be replaced. And no separate in-line "check valves."
IF the cockpit pump check valves and diaphragm are in good shape, the hose is totally without any pin holes or cracks, and the ends are all properly clamped, it WILL pump water.
(Now stepping off the soap box.)