Is Mysticism capable of being "experienced" by the use of the Intellect?

That is, can one's brain experience Mystical phenomena? I suggest it cannot, and my reason for saying this is that the term Mysticism is a label for that which the brain [being physical] cannot experience. And this naturally leads to the topic of "Intuition," which is a label for an aspect of the Soul, which is composed of Spiritual Energy. Can Intuition be proven via one's intellect? No, because no part of one's thinking is capable of perceiving Spiritual Energy.