But back to the title question, there have been several anarchic or nearly such societies in history. Three I can think of off the top of my head. Medieval Iceland and Ireland, and surprisingly, given my experience living here, Pennsylvania prior to the establishment of the Commonwealth.
Pennsylvania was full anarchy. The only difference (and what allowed it to be taken over) is that the Quakers were full-on pacifists, rather than the "porcupine pacifist" of a N.A.P. respecting anarchy.
That's not the only thing that led to the downfall, there was a lot of religious bigotry that resulted in civil strife. An irony, considering the main reason why most of the early settlers were escaping religious bigotry in Europe.