I can't see it happening; in fact, I think the Watchtower Society will change that teaching the same way they've changed many others.
Before the wars in Iraq and Afghanistan, I figured maybe it could happen - maybe the UN could knock off religion. After seeing what happened in those two wars - we can't even handle the Taliban without a lot of trouble, and they're still a threat and protracting the Afghan war, there's no way the UN, even with US backing, could somehow ensure that people would not attend religious services. There's not nearly enough reach or scope in the UN or US to do this.
Islam would probably be the biggest obstacle. It would become completely radicalized as its adherents fought such a ban. The UN and US are having enough trouble containing the small fraction of Islam that is currently radical. I can't imagine they'd want to take on the entire religion. They'd get a jihad like they've never seen.
I can also not imagine some evangelical US religions ever going along with such a ban.