No, another, more morally grounded culture, say, Islam, will take its place.
Leftists, secularists and atheists are cutting their own throats by trying to destroy the Christian foundation of our culture. A morally weak society will fall to one that isn't morally weak, even if the conquering culture is not righteous, but evil.
But, I guess in the case of the leftist/secular/atheists, they only believe that they are alive for 70 odd years and that no other portion of the timeline matters, as long as while they are alive they can do whatever they hell they want to.
What is it about Islam that you think would make it succeed where Christianity has failed?