Internal versus external battleship armor belts

Did battleships with external belts need thicker face-hardening because internal-belt ships could use the outer hull to absorb shock?

Not really; the outer hull was not the main armor, and the space outside an internal belt chiefly provided subdivision and volume rather than decisive shell resistance.

The outer hull of an internal-belt battleship is not expected to stop the incoming shell. The space outside the belt provides additional subdivision and usable volume. Equipment needed to keep the ship fighting should therefore remain inside the armor where possible. Cables and other systems outside the belt complicate that arrangement, since they remain vulnerable even when the protected interior survives.