Of course there would. But, it would be more up to interpretation by the parties involved. There would be less importance of a national "poverty level" or anything like that. But sure, it's human nature to band together to create classes. Even in socialist societies, you still see classes... they're just created and enforced by a state.
The idea that anarchism involves some sort of class-based revolt (a worker's revolution) is wrong. Anarchism is the ultimate limiting of government. True anarchism requires a level of objectivism that deals with divorcing one's personal feelings with policy. In other words, whether or not you feel that federal labor requirements or social welfare is a good thing or not, Anarchism does not deal with the virtue behind government intervention, it deals with how much of a limiting impact it plays on individual liberty. In the end, when you have a central body enforcing labor standards and class maintenance, you have authoritarianism, not anarchism. Whether production and property and the economy is controlled by a government, a church, a workers' union... it is still authoritarian, and thus, not anarchism. Syndicalists and so-called "Anarcho-Communists" miss this. They seem to think that, since the end justifies the means, it's okay for a central authority to exercise control in this manner. It's kind of like Republicans claiming to be small-government because they're economic liberals, yet when it comes to being big-government on civil issues, it's okay because they agree with that kind of control. It's subjective thinking. Whether or not you think control is justified has nothing to do with Anarchism.
It presents a paradox. People will assemble. It will happen. So, how do you protect an anarchist society from falling under a home-grown government (be it a corporatist presence or a synidcalist union)? Well, you can't. The only thing you can really do is to have a central government whose only role is to protect the internal geographical structure from outside interference. The rest is up to local communities on a voluntary basis.
So, I guess the quick answer is: Anarchism has nothing to do with class... it only suggests the absence of "national recognition."