It depends on what you mean by "damage". Humans have made a lot of other species go extinct. But damage to the planet itself? Hell no. Even if we did want to blow up the planet, I don't think that we could.
What I mean is that Earth will recover. New life will arise and thrive and very likely something else will get a chance at dominance. Or nothing will. There are no guarantees that what sparked human development will ever happen again. However, life, will go on. It’ll just go on without us.