The only honest answer right now is that we have no idea to what extent climate change will go.

There's life that will persist after humans, but what's to say the feedback loops will stop in time to stay hospitable to those?

Earth could be on track to shed it's atmosphere, or go molten - there comes a point where even the most resilient of extremophiles won't be able to persist, and Earth just becomes another completely lifeless rock floating through space.

Or we die off, the climate stabilizes, and everything's just fine for the critters that haven't gone extinct yet.

Or anywhere in between.

But we can't assume one way or another.

/shrug