Alfredo Bonanno defined anarchy as a tension to be lived every day in conflict with the established, non-anarchist order. That, at least, is how I read his writings.
I don't know if 7 billion people can live in a state of total anarchy. I believe that such a phenomenon will indeed require decivilization, and probably generations of healing from the toxic culture, as well as rotting of and forgetting how to use the physical infrastructure carved out of the landscape by civilization.
When Rome fell, Western civilization survived because the husk of the empire that it left was eventually re-used, and a large enough portion of humanity was domesticated enough where civilization could keep on turning. (Oversimplication, I know. Historians put me in my place please if I'm getting this wrong) The situation could easily be the same with our global civilization.
But I do think that it's possible for enough people to live anarchy where states are forced out of territories, cultures are infected with anti-authoritarianism, and such. So no, anarchy doesn't require decivilization, but I do think that it can more easily flourish in it and helps the process along.
edited to fix grammar