No. Often the car has had crash damage that has been repaired at a certified repair facility and does not show up on Carfax. Carfax is a good place to start, but does not replace a good 3rd party (independent) inspection by a qualified person. It also won't show how hard the vehicle was run, or how well it was maintained, which is a strong indication of how reliable the vehicle will be in the future and how long it should live. A good technician should be able to determine this information from a thorough inspection.