I don't know enough about Nozick's ethics to be sure the Freedom Monster applies. I imagine it would need to be more complicated than the utility monster thought experiment.
I'm not really philosophically libertarian anymore (the L has been getting smaller and smaller over the years), but I think someone like Nozick might make the claim that once the Freedom Monster takes over everything, it has a monopoly on the legitimate use of force, which makes it the state. One other way the Freedom Monster might not apply as an objection to Nozick's is that it seems to violate the principle of self-ownership by making everyone serfs. I think Nozick says we can voluntarily suspend or give up our rights, but what about children born into this situation? I just don't know enough about him to know what he would say, but the Freedom Monster does not strike me as an immediate knock-down argument against his political philosophy the same way the Utility Monster is of a certain breed of utilitarianism.
Most analytic moral philosophy hinges on positing ethical rules or maxims that explain our intuitions, quickly realizing that there are special situations where those rules or maxims entail an action or judgement that goes against our intuitions, then making a choice between biting the bullet or changing our account of morality. A lot of arguments, especially between utilitarians and deontologists like Nozick are basically arguments about which bullets are worth biting.
With regards to the bolded part, I don't think Nozick would be able to make this argument because if that were the case, then each new generation would necessarily be born with increasingly less freedom. He doesn't make that claim. However, the rest of this rings true, especially the part about the creation of the State. Anyway, I haven't gotten through Anarchy, State, and Utopia yet, but I thought of this while mulling over what I've read. Thanks for your insightful response!