Youmay find you develop callouses (thickening of skin) on the palm and palm side of fingers and this may reduce sensitivity a bit - not really sure if this would have any detrimental effect on playing. It would also be reversable by stopping climbing at any time. A protectve measure you can do is wear apprpriate high grip gloves for climbing. A good sports store should be able to help you. The change in muscle development as you strengthen up houldn't be detrimental. So why not do it!

On thing you should consider however, and this has nothing to do ith piano playing, given your age and gap in training you may be more prone to injury and overuse problems. Muscles may be prone to tears and also tendons- particularly iaround the shoulder joint but also arms, back and neck. I would suggest tou consider dong some training that would include a geeral weights program.