Maybe, for sure.
I'm not a religious person but I have experienced things.
Definitely a difference between tapping into the universe and being out of your head. You can be out of your head and not tap into the universe but unless you're out of your head it's pretty difficult to truly tap into the universe.
There are of course other ways of getting out of your head without ingesting psychoactive substances but they take many years of practice and dedication.
Humans have been ingesting psychoactive substances for millennia and I have a hunch that the experiences people have had whilst doing so has much to do with the formation of religious thought.
Anybody who has experienced such things whilst off their head will understand what I mean. Those who have never had any such experiences are more likely to be sceptical and suggest that such experiences are simply due to the dreamlike state that the chemical imbalance in the brain has induced.
Nothing can be proven either way, it is all down to personal experience; and you've either experienced something or you haven't.
As I said, some people experience things without psychoactive substances. But their experiences are usually dismissed by sceptics too.