System and method for maneuvering marine vessel with non-engine-powered propulsion device

A marine propulsion system includes an engine-powered propulsion device coupled in torque-transmitting relationship with an engine. A non-engine-powered propulsion device is coupled to a source of electric or hydraulic power. A control module is provided in signal communication with the engine-powered propulsion device and the non-engine-powered propulsion device. A user-operated input device is in signal communication with the control module. The marine propulsion system operates in a non-engine-powered propulsion mode in response to the control module determining the following: the engine was previously running; a speed of the engine is below an engine-stopped speed threshold; the marine propulsion system is on; and a request for movement of the vessel has been input via the user-operated input device. While the marine propulsion system operates in the non-engine-powered propulsion mode, the control module controls the non-engine-powered propulsion device to generate thrust to maneuver the vessel according to the request for movement.