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'Alright, I guess I am part of the House of Light now...'
In the end, Cedric decided to accept their offer and become the Holy Son of the House of Light. That said, he explicitly told them that this should remain a private matter for now.
From Cedric's point of view, it is way too early to make a splash. Besides, it contradicts his desire to remain low-profile. Sure, he could've used his other persona - Derrek, as a proxy, but he can't be in two places at once. His whole con is to confuse demons, besides, Derrek isn't trying to become a celebrity.
Still, he will cooperate with the House of Light. What Princeton and the Archbishop told him was true, with or without him, the House of Light had their own matters to attend to. They have tasks, goals, etc. He isn't required to take office and manage them directly, they can function on their own.
However, he did leave them with a gift that made the Archbishop incredibly emotional...
- Flashback -