This is a hot topic among the science vs. religion folks, with the answer generally being "no" as far as the pragmatists are concerned. In fact I've never seen an atheist acknowledge the possibility. So maybe this is a first. I said a big prayer one day, to a god I don't revere, and had it answered immediately and, so far, permanently. That was about three years ago, so it looks like a keeper.
Now I've seen the gag about how every prayer is answered, only most of the time the answer is "no." Cute, but it cuts no ice with me. This time it was an absolute yes, no room to doubt it.
Background: I'm Jewish on my wife's side. She's pretty secular as they go though--gets to shul for the holidays and that's about it. Most of her friends belong to the same synagogue, and she sits shiva and goes to their kids' bar/bat mitvahs. The basic stuff.
Me, I was brought up to sulk through Congregationalist service in the tiny town where we lived. There wasn't much compassion available, as far as I could see, and I could have used some then. Main thing goin on was smug. So I dropped the whole game as soon as I got out of town, at about 14. A few years ago I started doing yoga and some pranayama stuff, and heard the spirtual riff that generally goes along with that. I meditate (it works).
So a couple of years ago there was this Jewish wedding. On the way there my wife was complaining about something she didn't like that had/n't been doing. I have no clue now what it was, but as always at that time anybody who expressed disappointment about me aroused a very powerful and insurmountable sense of shame. This time was no different, except that I was heartily sick of it but felt that it was completely beyond my control. I couldn't do anything about it, and I'd been getting shrunk for some time.
We entered the hall where the wedding was to be. Just inside the door stood a small table with a pad, some pens, and a basket on it. There was also a sign that announced the revival of an old custom, no doubt related to the one Jews practice today at the Western Wall: they writer prayers, fold them up, and stick them in cracks in the wall for ha shem to read and answer. The sign promised that prayers written down that day would be placed beneath the chuppah (wedding canopy) where G_d would rain down blessings on them during the service. Apparently his aim isn't all it might be, since he's blessing the couple.
So, of course, I wrote "Uproot my shame", folded the note, put it in the basket, and haven't felt an iota of it ever since, and there have been plenty of occasions when I might have.
I haven't prayed since; don't want to push my luck.
So maybe this is a 12 steps effect, where you acknowledge that you can't lick your problem alone, and acknowledge that in front of a bunch of folks who share it, to some degree. Those conditions were surely met; the people there were Jews, most of them. The difference is that nobody but me knew what I'd written.
Later when I told this story to some friends my wife rebuked me because, she said, on such occasions prayers are supposed to be for the community, not oneself. Apparently ha shem doesn't share her view.