It would be a pretty bad investment considering studies of this already exist and are almost universally ignored. I also think you should say what you mean, where what you clearly want is a National Institute of Atheism.
I think people should refrain from thinking they can tell what I clearly want from what I say, as their error rate is high. You assume that I want an institute that will reach a foreordained conclusion, rather than one that will try to find correct answers. I hope you are in this case wrong.
Lots of charlatans spend lots of money advertising diets and health products that don't work. We have a National Institutes of Health that, among other things, funds studies that make more-objective pronouncements on diet and health.
Argue pro or con: It would be a good investment (payback would exceed opportunity cost) for the US government to create a National Institute of Theology, that would fund research into theological questions. For instance:
Everyone, religious and atheist, should be motivated to want the answers to these questions to become widely known.
(Yes, I know this would be politically impractical. Pointing that out is not interesting. What is interesting, is whether such a NIT would be beneficial, supposing it could be made.)