It's an interesting hypothesis. If welfare states make church social services unnecessary, do churches cease to have a deep role in people's lives/ Do they appear increasingly irrelevant to the poor? Here's a discussion of the strengths and weaknesses of a recent study on the subject. Money quote:
There's a statistically significant relationship between a Christian country's welfare spending as a percentage of GDP and the percentage of people in it who report attending church weekly, even when controlling for such variables as education and whether the country is Catholic or not. The weakness of the study comes not from its lack of data, but from flaws in how the variables are defined, failure to look for alternative explanations, and problems with individual case studies.