Apple juice may help a plant grow if the juice is all natural and has no added sugar, but it is unlikely to have any significant effect. Any beverage with added sugar does far more harm than good to the plant.
According to Gardening Know How, sugar absorbs water from the plant, interfering with the plant's intake of water and nutrients. Additionally, sugar can interfere with the nitrate balance in the soil and encourage the growth of pests.
Using juice on plants instead of water is never recommended. Citrus juices, such as orange and grapefruit juice, used on plants over an extended time is sure to kill the plants. The acid in these juices destroys the plant's immune system allowing mold, bacteria and fungus to enter.