No. Due to its basis in private property, "anarcho"-capitalism implies a class division of society into bosses and workers. Any such division will require a state to maintain it. However, it need not be the same state as exists now. Regarding this point, "anarcho"-capitalism plainly advocates "defence associations" to protect property. For the "anarcho"-capitalist, however, these private companies are not states. For anarchists, they most definitely are.
According to Murray Rothbard ["Society Without A State", in Nomos XIX, Pennock and Chapman, eds., p. 192.], a state must have one or both of the following characteristics:
1) The ability to tax those who live within it.
2) It asserts and usually obtains a coerced monopoly of the provision of defence over a given area.
He makes the same point in The Ethics of Liberty [p. 171].
Instead of this, the "anarcho"-capitalist thinks that people should be able to select their own "defence companies" (which would provide the needed police) and courts from the free market in "defence" which would spring up after the state monopoly has been eliminated. These companies "all. . . would have to abide by the basic law code" ["Society Without A State", p. 206]. Thus a "general libertarian law code" would govern the actions of these companies. This "law code" would prohibit coercive aggression at the very least, although to do so it would have to specify what counted as legitimate property, how said can be owned and what actually constitutes aggression. Thus the law code would be quite extensive.
How is this law code to be actually specified? Would these laws be democratically decided? Would they reflect common usage (i.e. custom)? "supply and demand"? "Natural law"? Given the strong dislike of democracy shown by "anarcho"-capitalists, we think we can safely say that some combination of the last two options would be used. Murray Rothbard, as noted in section 1.4, opposed the individualist anarchist principle that juries would judge both the facts and the law, suggesting instead that "Libertarian lawyers and jurists" would determine a "rational and objective code of libertarian legal principles and procedures." The judges in his system would "not [be] making the law but finding it on the basis of agreed-upon principles derived either from custom or reason." ["Society without a State", Op. Cit., p. 206] David Friedman, on the other hand, argues that different defence firms would sell their own laws. [The Machinery of Freedom, p. 116] It is sometimes acknowledged that non-libertarian laws may be demanded (and supplied) in such a market.
Around this system of "defence companies" is a free market in "arbitrators" and "appeal judges" to administer justice and the "basic law code." Rothbard believes that such a system would see "arbitrators with the best reputation for efficiency and probity. . .[being] chosen by the various parties in the market. . .[and] will come to be given an increasing amount of business." [Rothbard, Op. Cit., p.199] Judges "will prosper on the market in proportion to their reputation for efficiency and impartiality." [Op. Cit., p. 204]
Therefore, like any other company, arbitrators would strive for profits and wealth, with the most successful ones becoming "prosperous." Of course, such wealth would have no impact on the decisions of the judges, and if it did, the population (in theory) are free to select any other judge (although, of course, they would also "strive for profits and wealth" -- which means the choice of character may be somewhat limited! -- and the laws which they we