I firmly believe that the planet is more likely to survive ~ or, more precisely, that the planet is likely to survive much longer ~ than the human race.

The crap we're collectively doing may be making the planet less able to accommodate us, and lead to our extinction, but there will very probably still be a third rock from the sun, with or without lifeforms of some sort scattered over its surface and/or submerged in its waters (perhaps only very rudimentary at first).

If life is not completely extinguished, evolution may occur all over again ~ perhaps with somewhat better results. Of course, it hurts one's head to even try imagining such huge spans of time.