I do think the word avatar is going to come into its own in the third movie. The movie draws away from Jake who really was an avatar and more about the succeeding generation, the key character becomes or already is an embodiment of Eowa produced from Grace's avatar body and a possible unknown father (Unless they're REALLY going for the Messiah thing). Neytiri said that Eowa did not take sides in the previous movie, only to be proved wrong when Eowa finally did summon living things to defend either the Navi or the sacred space (possibly the same thing, to something like Eowa).
So if Eowa is the embodiment of the Gaia Hypothesis, then Kiri is the Avatar of the world-deity, just as one might theologically speak of Krishna being an avatar of Vishnu. All of Grace's memories are inside of Eowa's neural-network supercomputer, which also means Eowa has, in some ways, far more knowledge of Earth than Earth does of Pandora.
Cameron has said that future possible movies could take place on Earth and it's not inconceivable that they might go fill-on with the idea of introducing the Gaia Hypothesis back on Earth somehow, as well.
Jake is not navel gazer, but he got unusually insightful previously when he said, "We killed our mother and they're going to do the same here" -Jake Sully.