That you don't see a connection I will accept
But the connection I see from my perspective as a former christian is this:
Every time I ever prayed I never heard a thing. I tried and I listened, and some years I prayed every day and sometimes more than once. I always did what I should've as far as trying to contact god. But I never ever heard a single thing. I even payed close attention to the circumstances of my life. But I could never conclude that god was behind the things that were happening.
BUT
I always did notice that there was a voice coming from ME, guessing at what god might be trying to tell me. I would come up with a thousand things that I thought god might intend for me. But I didn't contribute them to god, because I knew they were from ME. I would suggest something in prayer, trying to ascertain, IS THIS WHAT YOU WANT, GOD? But nothing. Ever. My imagination trying to come up with god's will was all that was there.
My brother relates to me all the time about how god is speaking to him. He says he used to feel much like me. But he had an experience with drugs where he says he saw god. And this affirmed his belief. And now he says god talks to him all the time. He has described to me the way god talks to him. He says he gets a really deep feeling, for instance, that he should turn his truck around and go back to the house. And when he does, he finds something very important to his routine that he would've forgotten. Since he went back even though he doesn't want to only to find something he's glad to go back for, he attributes this to being god at work. He has used other instances. And they all sound like the feelings we get when our imagination tells us something that COULD be.
This is my personal experience. I think there is a definite connection between an overactive imagination and belief in god. In fact, at one time when I was a young teenager, I got the notion that churchgoers are at a constant battle to see who can pretend the best. And I don't even think they realize it. It's subconscious.
But these are just my experiences. And I've laid them out honestly (and in response to the "no connection" theory) for anyone's perusal. Please feel free to respond with your own peronal experiences, and do not feel that I am telling you you're wrong. I just want to see a myriad of opinions on this (and I especially want to see lots of responses to the original questions).