Can the center of gravity ever fall outside the mean aerodynamic chord?
Yes it can be. Whether the aircraft can fly with the centre of gravity outside this range is a different matter altogether.

When flying, the aircraft is balanced around the centre of gravity of the aircraft. Aerodynamic forces from the wing and the tail provide the balance, but up to a maximum. At some point the aerodynamic lift capacity of the tail is saturated.

In order to make sure that the balance can be achieved, the centre of aerodynamic force must be within certain limits of the centre of gravity. Or the other way around: CoG must be within certain limits of centre of lift, which is the better way to define it, making the CoG the variable.