This argument falls under the category of pragmatic arguments, as opposed to theoretical arguments, the latter of which seek to demonstrate the existence of God. Pragmatic arguments, on the other hand, merely seek to demonstrate that a person is justified in believing in God for practical purposes. Here's just one such pragmatic argument.
1. All things being equal, one should adopt a belief that leads to happiness as opposed to unhappiness. (Premise)
2. Belief in a God (especially one who is omnipotent, omniscient, and morally perfect) leads to happiness. (Premise)
3. There are no demonstrative proofs of God's existence or non-existence. (Assumption)
4. Hence, belief in God's existence or non-existence is on equal terms. (From 1 - 3)
5. Therefore, one should adopt and maintain belief in God. (From 1, 2 and 4)
Premise (1) seems intuitively true. I can't think of any arguments in support of it or against it off the top of my head, though. I'd support premise (2) by appealing to the many studies that show how prayer and meditation have a positive impact upon one's health and happiness. See, for example, this article. Praying to and meditating upon a maximally excellent God would seemingly add to one's health and happiness, considering that such a God would be in control and have a greater purpose for one's suffering.
Premise (3) is merely an assumption. I'm assuming for the sake of argument that there are no sound theoretical or demonstrative arguments for theism (I think there are) and no sound theoretical or demonstrative arguments against theism (I think there aren't). (4) follows from (1) through (3) and (5) follows from (1), (2) and (4).
Again, this is by no means a proof of God's existence. I'm also not claiming that people who pray and meditate won't experience suffering of various sorts. However, the same studies show that those who pray and meditate are generally more able to cope with these sufferings, which helps to explain why praying people tend to live longer, healthier and happier lives.