The NAV_CONTROLLER_OUTPUT MAVLink stream is configured in the stream list (mavlink_main.cpp:1454), but it never actually sends data on multicopters.
The stream's send() method in streams/NAV_CONTROLLER_OUTPUT.hpp only emits a message when there's a new position_controller_status uORB update. That topic is only published by the fixed-wing position controller (fw_pos_control), the rover controller, and the Ackermann rover controller. No multicopter module publishes it, so send() always returns false and the message never goes out.