Of course not, one is a political view and the other an economic system.
This "unified world theory" is not political or economic, but religious, consisting of the three elements listed, Islam, Judeo-Christianity, and Atheism.
For mixed metaphors, this is a good one.
So far the US has been a hold out, because of our strong religious faith. I suppose that we'll remain hold outs, but I don't know how exportable our system is. So, yes, the short answer is that secular capitalism is possible, but it will probably have more welfarist elements, and it's not "the American Way."
There's a possibility that the US will secularize without developing a bigger welfare state. Perhaps the great opportunities of financial success will keep citizens working hard, taxes low, and bureaucracy weak, even without transcendental moral sanctions, but I won't bet on it. Eventually it becomes too easy for the "have nots" to outvote the "haves" or for the "haves" to buy off the "have nots" by giving them what they want.
Another possibility is that global competition, mass immigration, or declining birthrates, will render European-style welfare states obsolete or unsustainable. Maybe they will collapse under their own weight. In that case, maybe the future will look American after all.