I don't think Anarchism could work. It relies far too much on people's honesty. While some will do the right thing by others, most would give in to temptation and just do whatever the hell they want. Then people who have been wronged will take their revenge, then the original person will get back at them... It goes on.
I'm a fan of Liberalism; people are free to do what they can to reach their full potential, and the Government/authority is to step in whenever someone is stopping themselves or others from doing so.
That being said, Anarchism could work on a very small scale, in a town where everybody knows each other and wouldn't want to hurt each other anyway.
That sounds good to me. Then if/when it fails, they lose it, point proven.
But then, since all these people desire anarchy, they wouldn't be a true reflection of the whole population. They could just be on their best behaviour in the hopes of ditching the government for good. The only way that could work is if it was a random group of people, not just those who want anarchy, and see how it goes.