I feel pretty sure there would be less, but I also feel pretty sure it would by no means disappear entirely. Faith isn't just about hiding behind something when things get tough, but its basic objective is also to explain everything. Everyone always gets into wondering the meaning of life, how things really came about, etc., etc., so the people who are more curious may go into faith anyway. On the other hand, people wouldn't feel pressured into escapism by seeking religious things that'll tell them that everything's under control, things will get better, etc...
I think that much makes sense... ^^