An acquaintance of mine, paleoanthropologist, regularly handles ancient hominid fossils - part of the job requirement. One day, while holding one of these objects (a skull if I recall rightly, but perhaps my memory is infected by imagery of people holding skulls in paintings and plays), he got a profound "areligious experience". Suddenly it hit him that he was going to die, and there would be nothing beyond his present life - his memories and self-awareness would simply disappear. In the future, the only thing that would be left of him (if he were buried, placed in congenial archaeological context, with an environment that isn't too dry, too acid etc.) would be a skull similar to the one he was holding, and perhaps a few large bones like the femora. Prior to this, the paleoanthropologist was already an atheist, but the areligious experience intensified his conviction that the natural world is all there is. His areligious experience was strong, non-inferential, and elicited in him a powerful belief in the non-existence of God--an experience in some respects analogous to religious experience.
Christopher Hitchens in God is not great argued that have some people have "blinding moments of unconviction that [are] every bit as instantaneous, though perhaps less epileptic and apocalyptic (and later more rationally and more morally justified) than Saul of Tarsus on the Damascene road." He does not present this as an argument from areligious experience, but he does suggest that areligious experience can be "rationally and morally justified." Just sticking to rational justification here, I am wondering what sort of justification Hitchens is thinking about. Suppose one is an externalist with respect to justification (or warrant). If God exists, there is a rather straightforward externalist route to warranted theistic belief on the basis of religious experience, by virtue of a properly functioning cognitive apparatus that successfully detects the divine presence (a la Plantinga), or by virtue of analogies between religious and perceptual experience, and by arguing that the religious experience, like the perceptual one, is properly grounded (a la Alston).
If God does not exist, then the human brain is the product of a purely naturalistic evolutionary process. I will here assume that the evolutionary argument against naturalism is unsound. Authors like Evan Fales have argued that we can expect that our metabolically expensive and complex brains produce, on the whole, more true beliefs than false ones, since it is more advantageous to have true beliefs than false beliefs. Under the naturalistic worldview, human cognitive capacities are truth-tracking. For example, our ability for induction, which we also use in scientific practice, could have warrant because it is the output of a properly working cognitive system, and the best explanation of why our cognitive system evolved the way it did, i.e., as a system that spontaneously makes inductions, is that nature is indeed uniform. So, taking this naturalistic account of properly functioning cognition (which is truth-conducive because of its selective benefits), a naturalist could say that naturalism is warranted because it is the product scientific inquiry, which is the result of a properly functioning, truth-conducive evolved cognitive apparatus.
Moments of unconviction have a spontaneous, non-inferential character. One plausible cognitive mechanism that lies on the basis of them is mental time travel. Humans, along with a few other species, have the ability to assess future scenarios or reminiscence about their experienced past. According to Suddendorf and others who have worked on mental time travel, the adaptive, proper function of mental time travel is that not that it allows us to recollect past events or project the future per se, but to enable one to anticipate and predict future events on the basis of past experiences. This allows us to construct possible scenarios, which can be compared in order to optimize future behavior. However, the proper evolutionary context of mental time travel is not to have a sense of what happens after one's death.
If metaphysical naturalism is correct, moments of unconviction are conducive to a correct belief, but I cannot come up with an evolutionary scenario where they could be somehow be properly linked to the truth of naturalism in an externalist way. If so, there is - at least for the externalist - a disanalogy between areligious and religious experience with respect to justified belief. While religious experience might be a source of warrant for religious belief, areligious experience cannot - it seems to me - have such a justificatory function.