In most legislations it is a legal requirement to carry one copy the Certificate of Airworthiness aboard the aircraft. As a point of law, the Flight Manual is part of the Certificate of Airworthiness. Ergo, it is a legal requirement to carry the Flight Manual on the aircraft.
Whether or not you use it for reference is for the company's own Flight Operations Department to decide. You should be aware that not all aircraft in the same fleet have the same technical and operational specifications. The differences are to be found in the AFM which is particular to an aircraft by manufacturer's serial number. Most companies edit the aircraft specific AFM data into the company Operations Manual as generic data applicable to all aircraft in the fleet; the AFM itself is not used as a live document.