I'd argue it's the other way around, that those seeking to change their lives for the better are a relatively self-driven minority and likely would have succeed

I'd argue it's the other way around, that those seeking to change their lives for the better are a relatively self-driven minority and likely would have succeeded with or without religion, religion was just a convenient vehicle due to widespread availability and approach-ability. It's anecdotal, but I was raised Baptist and married into a Catholic family (although neither my wife nor I are particularly religious). The people I've met in church over the years are no more or less driven than any other segment of the population I've encountered.