Can piercing damage be inflicted on a monster that is unaffected by monster effects?
The answer is yes. Piercing damage isn't an effect that affects the monster per-se, but it does affect the player. Think of piercing damage like burn that happens after the damage step, and just happens to be in increments of your monster's attack minus the opposing monster's defense. It is considered battle damage, but it's damage that is dealt to the player, not an effect that does anything to the monster.