Is The purpose of studying Kabbalah to reach the summit of humanity’s deepest desires – happiness, love, and peace and fulfillment?

Yes, but you forgot one very important word: that the summit of “humanity’s deepest desires – happiness, love, peace and fulfillment", is to be “Godly”. The Kabbala details the different attributes of God and His world, so that we know how to emulate Him ("imitateo dei"), to get the most out of our Godly souls.