Absolutely! I think it is common, and perfectly normal for people, at various developmental stages, to go through “profound” experiences. I assume it has something to do with changes in the brain. And it is also absolutely normal for people experiencing extreme environments or life-altering events to have unusual experiences.
I think I’ve written about this before on this forum, but I know after my mother’s death, in her home, I “felt” her presence over and over. I “felt” like she was just in the next room. Like I could call out to her and she would answer. Many people have this experience after the death of a loved one. A quick google gave me this.
http://www.after-death.com/Pages/About/ADC.aspx At about 11 or 12, I was absolutely certain that there were “ghosts” or “spirits” (dressed in Victorian garb) who resided in my home. I “felt” them all the time. I think that it is not uncommon for pre-pubescent girls to experience some sort of “spiritual” event. I googled “prepubescent girls and ghosts” and it is clear that ghost aficionados think that poltergeists are attracted to prepubescent girls. I think that there is probably something going on in the prepubescent brain that creates this illusions.
http://answers.yahoo.com/question/index?qid=20100416173818AAhcKGd And then there is something that seems to happen to a lot of people, usually in their late teens through mid-20’s. For me, I remember it so clearly. Long before the ruins of Tulum, Mexico became a mainstream tourist destination, there was a little campground just south of the ruins that backpackers would hang out at. I remember the night a group of us climbed up to the beautiful, ancient ruins, with a bottle of tequila (might have been Guatemalan aguardiente, actually-which is pretty hallucinogenic stuff) under the light of the full moon, and looked out over the sea. Sitting there, in the ruins of this ancient city, next to the ancient observatory that the Mayans used to study the stars, I imagined what life was like almost a thousand years ago, for the people who inhabited this beautiful place. And I felt them there, with us. And I looked at the stars, as they looked at the stars, and I thought about the size of the galaxy and the nature of the universe, and how little they understood, and how little we understand now. And I looked out at the ocean, and thought about the coral cities I had seen that day snorkeling, and how alien they were to any life that lives on the land, and contemplated the fact that life formed on other planets would certainly be much much much more foreign than the strange, unfamiliar landscapes that exist on planet earth. And I thought about life and time and space and communities and interdependencies and the process of seeking knowledge, and I felt as if I UNDERSTOOD. There, under the moon shadows cast by the ancient ruins, watching the reflections of the night sky on the flat, calm sea, I UNDERSTOOD. The connections. Everything. It was a complex epiphany, the details of which I don’t really remember.

What did I understand? I don’t know. But it was a profound feeling. And it motivated me. Motivated me to continue to work towards social justice, to learn, to respect the earth, to work towards building a world that would awe future civilizations, or even visitors from distant planets. So overall, it was a good experience.
I don’t think that these events in my life were the result of anything supernatural. But I can understand how people having similar experiences might use the supernatural as an explanation. There is so much about the human brain that we do not know.