Yes, in fact, it is encouraged to have pockets on your climbing shorts. You will need to carry an ID with you and you will probably want to have your phone. Try and find shorts that provide Velcro or zippers on the pockets, assuring your things will be secure and safe throughout your adventure. You don’t want to lose your valuables in the water or a hole. Try to find pockets that won’t absorb water, because you will probably stumble upon a stream or two, and it might even rain sometime along the way.