Religion is merely a set of social rules that have been around long enough to be incorporated into the faith. Laws are religion without the belief in a divine. One doesn't need religion to be happy, one merely needs to recognize what they have in oreder to be happy.

It depends on how you identify happiness. Some have a wider definition of this state or condition of happiness than others do. I know of several atheists and agnostics that will tell you that they are happy, but there actions and words indicate otherwise to me. I am not saying that I can deny that an atheist that says that he feels he is truly happy, is not as happy as he says he is. I have no means to get into his head or heart and measure his happiness. However, I am aware of the clear statement that Jesus made during his sermon on the mount at Matthew 5:3 Where he said "Happy are those conscious of their spiritual need, since the kingdom of the heavens belongs to them". What Jesus means by being happy, however, is not simply being jovial or mirthful, as when one is having fun. True happiness is deeper, carrying the thought of contentment, a sense of satisfaction and fulfillment in life. So those who are truly happy, Jesus shows, are people who recognize their spiritual need, are saddened by their sinful condition, and come to know and serve God. Then, even if they are hated or persecuted for doing God's will, they are happy because they know they are pleasing God and will receive his reward of everlasting life. I have to go along with the Son of God here and agree that the happiest people on earth are the ones who understand this statement and who truly live there lives in agreement with all of God's commands.

Saying religion is a "social reflex" is too simplistic. In spiritual terms, religion is our attempt to resolve the "big questions": who am I? What is the point of life? What is the basis for moral values? etc.. I think the best definition for religion is "that which re-connects us to the Whole". Most religions teach that the Whole is God -- a transcendent being who is separate from us in some way. Other religions teach other variations on what "the Whole" is. But pretty much all religions teach that an individual's relationship to the Whole is critical: that to be happy, one must have a healthy relationship with the Whole. This is a very abstract take on religion: there are many variations. But there is enough commonality among all the major religions to have produced many books on the subject. Huston Smith's "Religions of Man" is one very good starting point if you're interested enough. The answer to your question is that in some cases, people are "happy" but its a relatively shallow happiness which won't withstand much adversity. In other cases, people have resolved the deeper issues of their relationship with the Whole, and have done so without participating in "organized religion". But if you find these people and talk to them in depth, you'll find that they have dealt with the "big questions" very deeply, and that's the domain of religion.