Usually it does, in my experience. Faced with a problem you can't seem to solve, often the best thing to do is leave it alone for a while. It seems to keep simmering away in the mind somewhere, then when you come back to it, you get a fresh perspective. Prayer may help focus whatever the brain mechanism--metaphorically speaking--is that does that, but I don't find it useful or necessary to postulate that anyone's listening. It's just one more meditative technique.
I can do a similar thing if I am working on other things, without saying the Lord's prayer first and a solution is sometimes found. But if it is about something in the Bible I always use that prayer to start. It's no different to phoning the Ford dealership to get some info on a Ford product. I'm not going to phone a Chevy dealership to find out what size bolt I need for a For engine.
I consistently got zero, and sometimes even less than that, when things turned out completely opposite to what I was told to expect. Suppose you prayed for comprehension and insight, and the insight that came was "This doesn't make any sense." That's what I got. Pretty strange answer if that's what it was, and certainly not the way to sell the product, but of course I don't believe it came from anywhere but inside my own head. That's where I think your answers come from too (your head I mean of course, not mine), and you, in common with all religious believers, consistently misinterpret them as coming from outside.
I've probably got that , "This doesn't make any sense." on more than one occasion myself. In my case that was the correct answer as the original question was about the validity of the doctrine of a pre-trib rapture, any verses I ran into after that were pulling me away from considering that doctrine as having a solid foundation. Sure 1 or 2 or 3 could be point to that possibility but 10 more verses that covered that topic (when are people gathered) were against that view. It then boiled down to accepting what those verses said (and doing the follow-up work that is needed for any topic) or ditch those verses and going with what the majority of the people I was talking with were promoting. I always go with the verses, it may not be the one that endears me to the pre-trib crowd but I'm more than comfortable with the decision.
Here's an example that gives you an idea of just how complicated I can make 'arriving at a conclusion'
Part of the pre-trib thing is belief that there will be a 7 year trib, that is based on Daniel's last week of the 70 being split from the other 69. So I go and read that section but there is no 'flat-out' statement that says there is any break. Taking just that last week verse I go looking through the first 4 books of the NT to see if those things listed can be verified as happening just as listed.
The most obvious point is that in mid-week the end comes to sacrifice, that would have to be His death on the cross. So I go looking for the time given that shows Jesus preached for 3 1/2 years. The best book for that is John, it covers 3 Passovers, but the time given before that 1st passover doesn't add up to 6 months, it has it down to about a month at the very most. The other books aren't any help because they start (after Him coming back from the wilderness) His ministry after John is in prison, John puts that after that 1st passover. Hurdle #1, He didn't actually preach for even 3 full years. (This is where a prayer paid off) Back to Daniel's verse about that week. The 1st thing listed is that He would confirm a covenant, Okay who is 'He'? A covenant is a promise, to confirm something would indicate it is keeping a promise that was made some time before. At that point only God has been making promises to Israel. When it comes to sending a Messiah something is to happen before the Messiah, a witness has to be there. Zipping back to the NT and the book of John that is just what John is saying he is, and being a witness to the Messiah is one of the reasons that he is there. Jesus was baptized when He was about 30 (no ministry yet, just the baptism), John was said to be 6 months older than Jesus so when he was called he 'could have' been about 30.
So, using some math and some logic, can there be 3 1/2 years from when John was called until Jesus suffered the cross? They had a valid High Priest for a full 3 1/2 years, but it was a combination of time by 2 such priests, not just 1.
Examining the events after the mid-week is just about as involved so I will skip that for the moment. The other part needed is to look at the times given in Revelation, is there 7 consecutive years listed. Again that would take quite a bit of writing so I'll skip that for now.
In my opinion God did just what He said He was going to do, but He did it in such a way that it was not 'in your face' obvious.