The Federal regulation is pretty dang self-explanatory:
(l) Weapons and explosives. No person while on postal property may carry firearms, other dangerous or deadly weapons, or explosives, either openly or concealed, or store the same on postal property, except for official purposes.
Store the same (meaning the firearms) on postal property means in the car in the parking lot. The firearm is still being stored on postal property, it doesn't matter if your car is wrapped around it. The question is not whether you will get caught or not. The question was whether it is illegal or not.