It has happened in communist countries, and in these instances a great many of those who hold their religious beliefs are simply forced underground--not unlike how the early Christians had to meet in secret when the Roman government banned the Christian faith.
In other words, when one is dealing with having their freedom to practice religion banned, it would not make a great difference if the ban were world-wide or nation-wide. The effects would be the same on the individual level for one who would choose to practice their faith despite persecution.
So, if I awoke to finding that our country/world had outlawed religion, I would be quite upset. But I would certainly know I had a choice to make still, and would steel myself to pay that price.
A gestalt-type question to you, fish: if you were told you mustkeep your religion, or else lose all the relationships you value... would you be willing to do that if you felt that your religion was not the best represenation of truth, and you were convicted something was even better? Would you be willing to have your father and mother, wife or child, shun you or disown you if you refined your beliefs and 'changed up'?
You see, it isn't only banning of religion that is a problem, it is also using faith as extortion (Muslims do this, too, not only JWs). It's the other side of the persecution coin. Either way, a person still has a choice between choosing what to do--to gain/follow the world, or lose his soul.