As we know it, yes. It's safe to assume that Dousaku was a real person at some point. Still, in Doujun's quest to procure immortality, he lost his sanity and hallucinated his continued existence. The world of Sekiro is dark, and throughout your adventure, you'll interact with multiple characters who have lost their way and sanity upon drinking corrupted waters. Doujun is a symptom of the problems that plague Ashina, not the proverbial disease in and of itself.