It can exist but it can't last. Therefore, doesn't work. After the state of anarchy becomes a reality, people would organize in groups so they could take control of some space, resources and settle there to live. There would be territory disputes due natural resources, geography, weather. We can't grant that people will cooperate with each other, that people will live in peace because we know that the odds point to murder, thefts, rape, torture, kidnapping people(...)
Also, and to support the headline directly, this groups that would be created would grow as they eliminate the weaker groups and soon they would need someone or some little group to make the important decisions. A govern would appear. Anarchy would only be a form of killing people and changing countries borderlines so it can't never work or be allowed to be tried.