I think Julius fits right in.
He named himself for Julius Caesar, so between him being the Pope while this was painted, and him being an admirer of Imperial Rome, adorning him with Oak Leaves, placing a Cherub next to him, and having him carrying a book along with Plato, Aristotle, Parmenides, and Heraclitus seems to me to expression of respect or admiration, not derision.
Big picture, I'd be surprised if Julius II weren't in this. He would have been jazzed to have been included amongst the ancient philosophers whom he admired, and Raphael would have had motivation to patronize the Pope by including him among the greats.