I think he would find the time - a minute in a chapel on a base or a helicarrier or even in those rooms in a hospital after the immediate crisis is past and people are safe enough that he can catch a breath - rather than make the time.
It's a very fine distinction but I think that Cap's a true Christian. I can't see him as the type who, when hearing about someone who got flooded out of their home would go and pray - he'd go to their home and help them pick up the pieces.
He's not a "thoughts and prayers" type. When people need help Cap's not going to fold his hands and murmur vague well-wishes, he's going to put those hands to work.
We should be glad there isn't a preponderance of scenes with Cap pearl clutching in a church.