Jeff, Patrick:
I have never known that tree to come into play - even from a right-side teeing area to a right-side hole location. It's far enough to the right as to almost be growing into Cobbs Creek.
Now, IF the club were to extend the back half of the 13th green even ten feet to the right so that the creek would come in to play if someone were to (unsuccessfully) chase a "sucker pin" back there, then the tree would have to come down.
However, since that will probably never happen, I don't believe it's an issue.