A theocratic conquest of the world would propel everybody who survives into a new dark age.
A religious one would, but if God were in charge, that would not be the case by any means.
FWIW, the Founding Fathers were by and large religious men and established a government based on Christian religious principles.
It hardly threw us into any dark age. On the contrary, as we have moved away from it is when we started our downward spiral.