Can chemical peels help improve very dry skin?

No: Chemical peels use mild acids on the skin to loosen and remove the layer of skin called the stratum corneum which contains dead, damaged skin cells. Dry skin is usually related to lack of proper hydration of the skin (drink plenty of water, use moisturizers with neutral pH). Chemical peel will likely worsen the dryness of the skin due to increased evaporative losses from the skin.