I think you can find Christian mystics who embraced Jesus
"intimately", being that Jesus is God in the flesh, so to speak. Trying to extend a similar relationship to a supreme being seems problematic as it is seen as non-corporeal. And, even symbolically it seems vaguely incestuous.
Teresa of Avila wrote:
They deceive themselves who believe that union with God consists in ecstasies or raptures, and in the enjoyment of Him. For it consists in nothing except the surrender and subjection of our will - with our thoughts, words and actions - to the will of God.