Nope, anarchy is only the absence of a state. Like I said, it is still possible to enforce property rights in such a scenario… as long as you do it yourself.
This likely WOULD lead to less hoarding and more wealth distribution, because you cannot keep what you cannot defend. But it’s definitely wrong to assume all property would automatically become public and “free use” and everyone would share freely as in a communist utopia, because that requires agreement between people. And in the absence of a state, there is no authority that could enforce such an agreement.