No, energy drinks do not improve performance.
Mountain climbers lack oxygen. Energy drinks are drinks that contains high amounts of sugar. When such high amounts of sugar gets absorbed into one's bloodstream, their blood glucose level would increase tremendously. Therefore, the body would secrete insulin to convert the excess glucose into glycogen. Muscle cells would also start absorbing these excess sugars. This process involves the use of energy. Due to the lack of oxygen, lesser aerobic respiration could occur. Therefore, with the consumption of the energy drink, less energy would be provided for contraction and relaxation of muscles to allow the climbers to climb the mountain, decreasing their performance.