Note that this post is crystal-gazing.
I don't believe it will happen this way; if it did, I'd question what the hell happened in that area that made everyone anarchist! If anarchy is to be, each nation will become increasingly anarchic over time (assuming they have Internet access and favor bitcoin over their local currency) until the various states are too weak to entice their denizens into warring with neighboring nations. It'll then be a domino effect; once one nation collapses and its once citizens are now ruling themselves, so will another, and another, till a minority are people ruled by states; of course, I do believe some under-developed nations will attempt to go to war for "free land", but anarchism works like one gigantic nation: if you try to pick a fight with one people, the rest will hammer down on you, knowing the danger of going back to rule-by-force.
During this transitioning period, there would be two international communities, with one being those in support of the state, and the other being those who are not. The thing about anarchists is that they ostracize: they will refuse to acknowledge your existence until you meet whatever standard they've laid out. So the anarchists would not want to participate in the 1st international community, they'd create their own and do a "with me or against me" sort of thing.
Anyway, if an anarchist society occurred prematurely, it would quickly become a martyr; the only thing states have going for them is their brute force, and so conquering a society of anarchists wouldn't be an issue. Therefore, there would never be representation of a true anarchist society (perhaps a phony one but not a real one) in any kind of global governance conference, since they'd be annihilated before being invited.
That's a nice analysis. I assumed that eventually a critical mass of people who believe anarchy can work would be reached in a certain country which would then influence people in other countries by showing that society can function without rulers.