No, the local warlords would totally not be OK with just handing over land. But I'm sure both the local population and the world at large would be perfectly fine with it if Libertopia was as great as libertarians claim it would be; it would certainly be an improvement over the current state of affairs, which is essentially anarchy.
According to libertarian doctrine apparently the citizens will band together effectively to defend their newly-claimed territory, and this defense will somehow magically occur with a tax base near zero, because an all-volunteer force will be both well-equipped and well-organized, even with nobody on the hook to actually pay for any of it.
Yes, they would totally encounter some sort of outside force (and probably inside forces) that would try to destroy the fledgling nation. Defending your borders and providing for internal security is what makes a nation a nation; it's kind of silly for libertarians to argue that their ideas would work great if only they didn't need to do those things. Yeah, and communism would work great if only people would produce what was needed with no incentive to do so. And fascism would work wonderfully as long as it could be ensured that no raving lunatics could take charge, etc.