I don’t believe that the Holy Spirit actually joined to the nature of a dove, so if an observer pointed and said, “Look, a dove!” he would have been mistaken.
Nevertheless, if he had pointed and said, “Look, the Spirit,” he would have been correct.
Of course, “The Angel of the Lord” appears all over the place in the Bible, especially in the book of Judges. Before kings were put in office, Israel seems more or less like a Narnia with Aslan appearing and disappearing to deal with various problems in the nation. But Hagar and Abraham and Jacob also meet with a figure who seems to look human and then is revealed to be God. Thus, in Genesis 18, Abraham meets God and two angels as human beings in appearance.
My point here is that the incarnation, while new, is not that surprising. God showed the ability to unite Himself with creaturely traits (such as location in space) from the very beginning.
In fact, when we are told that God breathed into Adam’s nostrils, the easiest way to understand in passage in context is that God appeared as a man like Adam giving him mouth to nose suscitation.