It likely will. But in a sense, we already live in an anarchist society. For example if police come to arrest you for growing cannabis, you can always get your bazooka out and defend yourself against the aggressors. And you'll realize no one rules over you. Then you'll probably need missiles to fend off the helicopters and fighters that will undoubtedly follow. Most people, out of convenience or a lack of resources, choose not to.

Bitcoin will likely change the balance of power and weaken the state, and make our right to defend ourselves from NAP-breaching aggressors more enforceable.