While I don't entirely think this article was brilliant, it seems to be getting downvoted in excess of what seems appropriate. Not entirely sure why that is, although a bad choice of example probably helped push it along.
To answer the main question: need more information. I mean, it depends on the degree to which the negative effects happen, and the degree to which it seems this new belief will be likely to have major positive impacts on decision-making in various situations. I would, assuming I'm competent and motivated enough, create a secret society which generally kept the secret but spread it to all of the world's best and brightest, particularly in fields where knowing the secret would be vital to real success. I would also potentially offer a public face of the organization, where the secret is openly offered to any willing to take on the observed penalties in exchange for the observed gains. It could only be given out to those trusted not to tell, of course, but it should still be publicly offered; science needs to know, even if not every scientist needs to know.
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.)