Very very interesting, and I think your hypothesis is very strong.

I would, however, present Russia and other eastern European nations as counterexamples. In Russia, Ukraine, Belarus, and the Baltic states, which used to be part of the Soviet Union, populations had become largely atheistic by the late 20th century. The trend began with official Soviet repression of religion, but it took genuine root. Most people tended to be sincere atheists.

But after the Soviet Union fell in 1991, several former Soviet republics embraced one particular form of Christianity or another with strong state support.

Russia, for example, established the Eastern Orthodox Church as a sort of de facto state religion. The government actively encourages and supports Orthodox churches while using various not-quite-repressive methods to discourage other churches. You can see a similar process in Ukraine.

The result has been a strong resurgence of Christian belief. Populations that were overwhelmingly atheist now feature large pluralities of Christians, and church attendance is growing not falling.

I might also present the 4th and 5th century Roman empire as a counter example. ;-)