Yes, he does make all those references to Oblivion events in that quest inside Pelagius' mind.

But I wonder if he merely remembers that those events took place but not his real involvement in them, and as far as he's concerned there has never been a moment when he was not Sheogorath.

Or maybe he does know he was the Champion of Cyrodiil/Hero of Kvatch at some point, but would never openly acknowledge that. Instead, he would rather vaguely mention it in a playful fashion.

He likes to pretend he was the champion on occasions, but he's Sheogorath now...or always was, but only when he wants to be. Hes kind of crazy like that.

My CoC didn't partake in the Shivering Isles, though my Listener did. Now hes a hole in the shape of Sithis, and that suites him just fine.

He has more important things on his mind. For example, Cheese for everyone.