I was talking about depression and anxiety in the regular senses, not just the clinical ones. Mental disorders can certainly cause delusional or otherwise distorted thinking. If you're clinically depressed, that can cause a narrowness of mental processes. But these disorders may have neurological causes.

If you're talking about cognitive behavioural therapy, I'm sure that brainwashing yourself or radically changing your thought patterns can have positive or negative impacts on your life. I don't see why that wouldn't be the case. Different ways of thinking can certainly have different emotional or social effects.

But the question you raised is whether atheism or theism is due to cognitive distortion. Who sees the world more clearly, the atheistic naturalist or the average theist? Both sides will say they do, of course, since they think they have the truth on their side. But that's a philosophical, not an empirical question.

Bringing psychiatry into the mix isn't so helpful since the psychiatrist's definitions of mental disorder are socially relative, as I show in several articles. Psychiatrists don't classify religion as a mental disorder because having a disorder has to cause suffering and it has to impede your ability to perform your social functions.

But if we're talking about a delusion in the abstract, it's obvious that theism is much more deluded and irrational than naturalism. Again, that's a philosophical claim, not an empirical one, unless you can show that religious people tend to be smarter than atheists. Good luck with that.

The links I provided show why an intellectual would likely be less happy than someone who doesn't know any better. That's largely a matter of commonsense. Intellectuals can overanalyze and are more likely to see through the delusions and conventions that sustain social unity. That lack of social conformity can be alienating, which negatively affects the smart person's wellbeing in various ways. It's quite possible to be too smart, inquisitive, and sensitive for your own good, especially when the social order tends to be supported by myths and prejudices that don't withstand much scrutiny.

Once again, these are philosophical rather than strictly empirical matters to be settled with a bogus study that can't likely be replicated in any case.