I'm a newbie.
I'm generally sympathetic to the pragmatic benefit over "scientism" (i.e., ignoring actual empirical effects based on what simply must or couldn't be the case) view. (In fact, I plan to post a little piece on that matter shortly.) I'm a fan of the so-called "tetris effect" of learning how to be happy by doing/noticing.
I make a distinction in the case of theism/atheism for two reasons, though. First, not to put to fine a point on it, theism is too wacky/undefined. Religious people tend not to really have any idea what the hell they are asserting when they say they believe in God or providence or whatever. An "omnipresent force," "a benevolent watcher," karma, Jesus, Jesus's old man, Vishnu, the tao, a first cause--who the hell knows what they are talking about. Second, I think you can get the same psychological benefit (which I don't doubt) without any of the cloud cuckoo land.
What used to be called "positive psychology" got a bad name around the time of Freud because it became increasingly clear that it in't as successful at helping people with serious mental problems ("hysteria") as drugs, the talking cure, shock therapy, etc. What it is good at is increasing (a bit) the the quotient of general happiness in the practicer. And the thing is, religious practice isn't so hot at fixing psychosis either. They're about on a par. But utilizing the "tetris effect" doesn't require one to believe anything...well...stupid. It's just a practice, like meditation, that makes one feel better.
In sum, my feeling is that there's no harm in getting these benefits--even if they're something of a Pollyanna/placebo thing. But all else equal, if you can get such benefit without the use of bronze age fairy tales, that's the route that makes more sense. If your hypothetical were adjusted slightly to insist that there is no other way to receive the longevity and happiness provided by "theism" (whatever that is, exactly), I might revise my answer. But I think I'd still want to know precisely what bilge I'd have to swallow to get this increase in utility.
W
Suppose it is absolutely true that atheism has a negative impact on your happiness and lifespan. Suppose furthermore that you are the first person in your society of relatively happy theists who happened upon the idea of atheism, and moreover found absolute proof of its correctness, and quietly studied its effects on a small group of people kept isolated from the general population, and you discover that it has negative effects on happiness and lifespan. Suppose that it -does- free people from a considerable amount of time wasted - from your perspective as a newfound atheist - in theistic theater.
Would you spread the idea?
This is, in our theoretical society, the emotional equivalent of a nuclear weapon; the group you tested it on is now comparatively crippled with existentialism and doubt, and many are beginning to doubt that the continued existence of human beings is even a good thing. This is, for all intents and purposes, a basilisk, the mere knowledge of which causes its knower severe harm. Is it, in fact, a good idea to go around talking about this revolutionary new idea, which makes everybody who learns it slightly less happy? Would it be a -better- idea to form a secret society to go around talking to bright people likely to discover it themselves to try to keep this new idea quiet?
(Please don't fight the hypothetical here. I know the evidence isn't nearly so perfect that atheism does in fact cause harm, as all the studies I've personally seen which suggest as much have some methodical flaws. This is merely a question of whether "That which can be destroyed by the truth should be" is, in fact, a useful position to take, in view of ideas which may actually be harmful.)