I'm thinking that the answer to your supernatural experience question is: No, but to understand that one has to learn about God's Spirit. That answer is way too long to go into here but I will touch on it.
However, you mentioned "living water".
The first reference of living water is from Jeremiah 2:13 where God said that He is "the spring of living water" (NIV). John describes "the river of the water of life flowing from the throne of God and of the Lamb". (Rev 22:1, NIV)
A spring is a source, and living water has been described as life in Rev 22.1. I understand God saying to us in Jeremiah 2:13 that He (God) is the source of life.
In John 7:38 (NIV) Jesus is telling people that if they believe in him as Scripture has said, streams of living water [LIFE] will flow from within them. I believe Isaiah 43:19 is the prophesy Jesus is referring to, as Jesus is the way in the wilderness, and streams of living water (Life) will flow from those who believe in him. This will happen with the gift of God's Spirit.
I made a pretty in depth study of God's Spirit and I feel like I can describe Him in two words: Loving Caregiver. God gives us His Spirit to help us learn who and what He is, and who and what we are. In learning about God and living what we learn, we begin to live the life he wants for us to live. We do this in steps and as we live, others experience the life we have.
Paul wrote to the Church of Corinth and said, Therefore, if anyone is in Christ, the new creation has come: The old has gone, the new is here! (2 Cor 5:17)
God lives through His children to bring life to others. God's life flows to others through His children and His Spirit shows us how to do this. Consider that God's Spirit is the primary caregiver of His children.
On a side note, I can see that the broken cisterns mentioned in Jeremiah 2:13 are made new through Christ (see Acts 2).