We're unlikely to reach the worst case scenarios where most of the world becomes unliveable - but we're already starting to approach the point where certain countries become unliveable due to extreme heat waves and lack of water, or at least incapable of sustaining their current population level. Which wouldn't be that much of a problem in a world with no borders where those people could just move elsewhere, but in the real world, that means the more we let climate change get out of hand, the more mass migration we'll see, on a scale that dwarfs everything we've seen so far.