No such thing as "naturally occurring sodium", it is way too active for that.
Would it be different for any other metal? Say, piece of iron?
In a way you are right, we can think about the piece of metal as if it was cations in the sea of electrons. Trick is, it is perfectly neutral, and when you try to remove any of the atoms it comes out as neutral, which exactly as many electrons as it should have. Removing these electrons is a separate process of oxidation.