BECAUSE MYRIAD LAWS INTERACT THIS IS NOT AN EASY QUESTION TO ANSWER.
Everything seems to come down to when is a federal law not a federal law, and which has more force: a federal law, a federal regulation, a state law, or a local ordinance? All of the king's horses and none of the king's men have a genuinely definitive answer.
Consequently, it's a pretty good bet that an otherwise legal and licensed firearms carrier may reasonable expect to come up short and be caught in the tangle of laws, regulations, and definitions that apply to the ambiguously defined entity of the United States Post Office.
In this instance, legal or otherwise, it appears safe to say that the government mentality - either local, state, or federal - is to screw anyone found to be in possession of a firearm on postal property. I'm NOT saying this is the right, or the necessarily legal thing to do; but it is how a gun carrier might reasonably expect to be treated, 'by government' over any incident of post office carry.
The thought has occurred to me that: If I am ever shot or murdered by a homicidal post office employee - or someone else who's, 'gone postal' - while I'm on post office property, do I or my heirs have the right to sue the government for either compulsory (and capricious) disarmament, or because of a (de facto) failure to adequately defend?
(You can't say that something like this would never happen BECAUSE it already has! Probably not, though, huh!)