The push would have to be quick yes, because it would run out of supplies, become stretched, exhausted, and if it did not blitz ahead they would likely be pushed back and stalemated.
Well, here is a quick map I did up of a possible outcome with all these religions.
Key:
Peach-Buddhism
Orange-Nestorian Christianity
Light Blue-Celtic Christianity
Purple-Zoroastrianism
Teal-Aztec/Inca
Green-Native American
Yellow-Egyptian Polytheism
Black-Tribal/Other/Unknown
Fine, also add Aztec/Inca beliefs (whatever you call that), Iroquois/Northeastern Native American beliefs (whatever you call that), Egyptian polytheism, and lastly Celtic Christianity. :D
Well, the difference between invading the South and destroying its economy versus invading the North and destroying its economy is a large one. Think of all the population differences and how the Union could quickly raise up volunteers all across the populous industrial heartland to resist this...
It's actually not very American at all because what the American religious right wants us to believe is that anything that is non-religious is run by evil god hating secularists.
Actually if you look on it at a global scale the world is mostly religious.
Better the UN than the British troops that shot Irish for fun then drank with the protestants! Of course the British stopped slacking off after the bombings in Belfast and Antrim bombings in 1991 and of course the Magharra bombing in 1995, that one had some of the highest casualties.