I think the planet will be fine, but life on it will be tested. Then again, that's how things have always been. 500 years is a short geological timespan, so there may not be any supervolcanic explosions or major shifts in the Earth's crust that cause massive changes and large scale death and destruction. And the next major meteor strike might still be millions of years away. Or a week...
I do wonder if the world will be in some backwards state due to a war or other man-made cataclysm. The human population is still growing, and that means a need for more resources (food, land, clean water, etc) and a greater temptation to take what is needed by force. I'd love to think that we'll end up solving all of our problems and building a utopia, but our minds aren't built that way and we won't have evolved enough in 500 years to fix the many issues that keep us from taking that next step.
On the other hand, we'll have technology that can display a movie directly on your retinas and deliver sound directly to your brain. So we might not even notice that the world is disintegrating around us.