Good question. I think we will survive, we are good at this, but the living conditions may become more difficult if we keep going. We are already finding better ways to manage our environment, and a lot of progress was made by the previous two generations. There is more environmental laws in developed countries for example. The problem is that, as you know, we take a lot of time to see and reduce our impacts on the environment and on ourselves, sometimes when it is too late!
I think survival and quality of life are important to talk about. Humans, as Maxime pointed out are likely to live for a very long time, and probably survive past disease outbreaks, ecosystem destruction and climate breakdown. Surviving is not enough necessarily and this means that not everyone will survive and we will have to compete for food, water and places to live. I am not a climate scientist, but these sort of situations are already happening in hotter parts of the world and in the Arctic Circle, where indigenous people have to move to different areas/countries. So how long will it be, before this happens? It depends on how fast we act addressing climate breakdown