Wow, I really like this idea. I don't personally subscribe that putting the elements (or whatever the necklaces and the crown things are) back into the tree gives back the elements from the Mane Six; they're already tied to their element. Giving back their necklace seem to me that it just means they can't channel their element; it doesn't mean their not connected to their element anymore.
Although, Appley did pose concern that their friendship connection would be hampered by giving the elements back to the Tree of Harmony, so they'rs that. But wait! The Mane Six didn't start with the necklaces; they were connected to their element before Twilight gave them the actual necklace.
That is quite an interesting point.
So! Overall, I'd have to say that each of the Mane Six probably are the corporeal incarnation of the actual element, and the necklace is just the way the Mane Six channel their element.