Another wild JAA question?
Engaging the autopilot will not change the aircraft’s inherent stability; and even if the aircraft has stability augmentation e.g. Mach Trim, that system is more than likely to be engaged in manual flight as well as auto flight.
Selecting an autopilot ‘on’ will normally engage the existing flight guidance system (FD) modes or, if none selected, the autopilot basic pitch and roll modes. The basic modes are type dependant, usually attitude hold (Pitch and Roll), or a combination of Roll, Hdg Hold/Select with Vertical Speed.
Thus What happens when you engage an autopilot in terms of stability enhancement? … nothing.