Well, evidently he did, because the stories of Rahula and his inclusion in the Sangha have an appearance in the suttas.
What is potentially up for grabs is the specifics surrounding his departure into the homeless life. In terms of Buddhist hagiography, it's often hard to separate fact from enthusiastic embellishment.
Agree that there is no doubt that he left. The popular story of him stealing off in the night leaving a sleeping Yasodhara and Rahula appears in the Commentaries. The suttas record him as saying that his parents cried when he left the palace to renounce. But I can't remember the particular sutta. While I try googling, perhaps someone will be able to recall it.
Edit: Ariyapariyesana Sutta (Majjhima 26)
"So, at a later time, while still young, a black-haired young man endowed with the blessings of youth in the first stage of life — and while my parents, unwilling, were crying with tears streaming down their faces — I shaved off my hair & beard, put on the ochre robe and went forth from the home life into homelessness.