Does enlightenment in all teachings amount to a progressively deeper realisation that I am already enlightened?

So e.g. kensho is usually thought of as beginning realisation in zazen, and is into our true nature as Buddhas. Does enlightenment in all teachings amount to a progressively deeper realisation that I am already enlightened, or is that only true in hongaku theory? Is it the case in any / all Theravada Buddhism, in Tibetan Buddhism, etc.? Not asking about gradual / sudden polarities, or about any other scheme to think about enlightenment, only whether **every single enlightenment we can have in Buddhism is *of our intrinsic enlightenment***. ---------- I seem to be attracted a lot of off topic answers about whether anyone say they themselves are enlightened. I have confirmed through google that the Buddha did say "I am to be enlightened", at least, and Huineng did say "I am enlightened". Also in Mahayana sutras he claims "The Tathgata... chants these words: I am the Tathagata (etc.)". Isn't the "conceit of I am" a specific thing, the idea that I will either exist forever or be annihilated, that I am the same from moment to moment, or that anything can truly belong to me until I am a Buddha? > Conceit is developed with regard to one's possessions when there is > misconception that they are enduring and permanent. The material qualities of eyes, ears, visible forms, are wrongly held to be permanent and consequently vanity is built round them.