Of course, if humans went extinct by the processes that we know of, instead of just quietly vanishing, there would be damage to the Earth that would take extensive time to repair. Nuclear winter, asteroid impact, climate change extreme enough to make the world actually unliveable for humans, would all have major effects on the restorative capabilities of the natural ecosystems.
On the other hand, a truly "renewable" human infrastructure might look reasonably intact after a year. Solar powered electrical systems run by computers, water supplied from local cisterns, located in a region that does not freeze in winter, might continue to provide services after a year. Sure, these things eventually require maintenance. But, there are places where people can live without much infrastructure (e.g., Amazon rain forest), and also places where human infrastructure is essential to human habitation (densely populated cities in regions that freeze).
Which brings up a point about whom to blame for CO2 emissions. Comparisons of per capita emissions by region are not that useful for a couple of reasons. First, the amount of energy needed per capita depends on the local climate. Second, the energy expended to produce the goods and infrastructure for one location might actually be expended in other locations. For instance, China makes a lot of the goods used in the U.S., Canada and Europe, and most of the technological goods used in Africa come from outside Africa.
Also, it is useful to realize that a lot of the people in the low per capita CO2 emission regions are simply not affluent enough to live the lifestyles of people in the higher CO2 emission regions, but they aspire to those life styles, so efforts to create "equity" among the regions are, in effect, efforts to create more CO2 emissions on the behalf of those in the "less developed countries".
To me, the bottom line is that humans need to learn to control our population densities by voluntarily controlling our own reproduction rates, so as not to have them controlled by wars, famines and pandemics.