As I understand it, metallic static shielding bags act as a Faraday Cage
No. They are neither conductive nor thick enough to effectively block electrical fields.
which protects the contents against external electrostatic discharges
They do, but mostly because they're OK insulators between in- and outside.
A normal plastic bag works better than the antistatic bags at this: there's never a path through the contained electronics that is of lower or comparable resistance as along the outer surface of the bag for a good insulator.
However, does this stay true if for example a PCB is wrapped in plastic or paper before being inserted into a metallic static shielding bag which is then sealed?
That sounds more like a ESD endurance test than antistatic packaging:
Static electricity will form on the insulating packaging material due to friction surface effects, and one unlucky shift of weight suffices to make the board be the electrically easiest way for built up charges to travel - either to oppositely charged surfaces, or through the board to the metal box.