This would be a very unusual scenario, but it is possible. The heart is composed of cardiac muscle, which is different from the other types of muscle found in the body. Smooth muscle and skeletal muscle both require stimulation which originates in the nervous system in order to contract. Cardiac muscle, by contrast, is self-exciting. Consequently the heart can contract without receiving any instruction from the brain to do. Because of this, the man in question could survive, with his heart beating on its own.
However the nervous system controls the heart rate; in a normal person, the heart does not always beat at the same speed, but rather it speeds up and slows down in response to exercise, changes in body temperature, and emotional state changes. The man in this question would not be able to engage in vigorous exercise, because his heart rate would not rise to accommodate his body's increased oxygen needs.