Quoted from Noah's Chapter 5 Story Quest "Righting the Wrong": Yes! I still have the power of the Moon that the imposter injected in me. Even if it mutated just like my power of Darkness, the fundamental property of regeneration should still remain.
Noah's main story path is Liberator, so since his moon power is mutated in that path as well, his moon power wasn't mutated by Clamor's Celestial Magic.
Edit: It's also a mention that the Order injected the moon power into him.