You start on a beach. You go to the moon. You come back. You go to Hollywood. You then go to the summit of Mount Everest. Have you increased your gravitational potential energy more than if you had climbed to this summit without all the other side trips?
The gravitational potential energy of a body with mass m is given by m*g*h where g is the acceleration due to gravity and h is the height of the body.
If a person starts on a beach, goes to the moon, comes back from the moon, goes to Hollywood and finally climbs Mount Everest to reach the summit, the gravitational potential energy of the person is only dependent on the person's height when on the summit. The movement prior to the this is not relevant as it does not affect the final potential energy of the person.
The answer to the question asked is that the person would not have a higher gravitational potential energy if the movement before climbing the mountain had not been made.