Dunno... It's a strange thing to think about. If Immortality is truly reachable in this lifetime, I see it going down and completely destroy this planet for good. I mean, I myself fancy the idea of it. However, with the amount of people we currently have, a form of population control will be needed to put into place. Without that control, you might as well say fuck it, and go die right then and there.
Something will happen within our life-time. But when whatever it is does happen, how quickly does this world collapse?