For the most part, we cannot really say that religion has had a great influence on population patterns in the Americas. It has had some impact in that it has caused people to come to the Americas. It has had some impact in that it has affected exactly where in a country or in a city people live. Outside of that, however, it has not had a major impact.
Many people have left various countries and come to the Americas because of religious persecution. Perhaps the greatest example of this was in the late 1800s and early 1900s. At that time, many Jews came to the Americas (in particular the United States) because of things like pogroms in their home countries of Eastern Europe. They saw the US as a country in which they could have both religious freedom and economic opportunity. This has affected population patterns in the sense that it has increased the overall population.
Religion has also played a role in determining exactly where specific people chose to live. For example, Jews who migrated to the US tended to settle in cities. More specifically, they tended to settle in places where other Jews already lived. They wanted to be near to their coreligionists to form communities that felt comfortable to them.
Thus, religion has had some impact on population patterns in the Americas, but not nearly as much impact as other things like economics have had.