Not necessarily. If the state were replaced tomorrow in a given geographical area with multiple options for various functions typically performed by governments (police, arbitration, schooling, etc...) and people had to pick which they used, the so-called followers could simply pick wantonly or follow someone else's opinion - much like people do for car insurance in the US. There would be no State regardless of whether or not the populace thought themselves to be anarchists. There would likely also be collusion amongst a subset of service providers to retain their markets (for policing, schooling, etc...); despite the inefficiency in such collusion, it would also apply a basic order to geographical region.

A plurality of the populace having anarchist views is not necessarily sufficient for anarchy; the availability and use of non-state alternatives to state activities is the required element. That may occur due to the work of an agitating minority and due to a weakness of the state as it inevitably deals with the aftermath of having to reckon with currency and debt issues. Minarchism and later anarchism may be foisted onto the people whether they want it or not.