Do atheists encounter God when they stop believing in God?

"In the New Testament faith means surrender to God. Those who say, 'I can't believe in this God,' usually mean, 'I cannot accept the particular tenets of the religion of my childhood. They were not something I feel I could identify with.' But that does not mean that they don't have faith. An atheist is really someone who has another religion. For them God is not God. But since God transcends all concepts anyway, it really does not matter that much whether you think of God as God or God as not God. For faith it does not matter, because even if you have a belief system that calls the Ultimate Reality by some other name or label, anything you can say about God is more unlike God than God actually is." -- Fr. Thomas Keating in  Divine Therapy & Addiction

If we take what Keating says seriously that many people are asking for something based on a specific preconception of who and what God is and how God operates. If I haven't written it somewhere before, I would expand this and say if you have experienced true joy, beauty, the thrill of discovery, freedom or liberation from shackles of the body, heart or mind, then you have awoken to/realized part of God (or your experience within God).

Take this quote by Robert Ingersoll which sums up what many agnostics and atheists feel:

When I became convinced that the Universe is natural--that all the ghosts and gods are myths, there entered into my brain, into my soul, into every drop of my blood, the sense, the feeling, the joy of freedom. The walls of my prison crumbled and fell, the dungeon was flooded with light, and all the bolts, and bars, and manacles became dust. I was no longer a servant, a serf, or a slave. There was for me no master in all the wide world--not even in infinite space. I was free--free to think, to express my thoughts--free to live to my own ideal--free to live for myself and those I loved--free to use all my faculties, all my senses--free to spread imagination's wings--free to investigate, to guess and dream and hope--free to judge and determine for myself--free to reject all ignorant and cruel creeds, all the "inspired" books that savages have produced, and all the barbarous legends of the past--free from popes and priests--free from all the "called" and "set apart"--free from sanctified mistakes and holy lies--free from the fear of eternal pain--free from the winged monsters of the night--free from devils, ghosts, and gods. For the first time I was free. There were no prohibited places in all the realms of thought--no air, no space, where fancy could not spread her painted wings--no chains for my limbs--no lashes for my back--no fires for my flesh--no master's frown or threat--no following another's steps- -no need to bow, or cringe, or crawl, or utter lying words. I was free. I stood erect and fearlessly, joyously, faced all worlds.

It sounds like many people may perceive (an aspect of) God but don't realize it because of their certainty about who or what God is. (This isn't an attempt to impose God on those who claim to not believe, it is a perspective that assumes the reality of God and the sincerity of atheists.)