Deckard can't be a hero. From the start, he is coerced into action. Only at the end of the story does he become Rachael's hero, but there is no conflict there, the twist is that Gaff (Edward James Olmos) lets the two get away, thinking Rachael will die soon.
Deckard hadn't faced a nexus 6 replicant, who were supposed to be at least as intelligent as the scientists who created them, which Roy Batty proved in the 'Meet Your Maker' scene.
So Deckard is hopelessly outgunned intellectually. The replicants are also far more combat capable. This is the usual case for Detective/Mystery stories (Watch Chinatown).
A very nice twist in the film is the climactic Thriller scene. In a Thriller, the main character must be at the mercy of the bad guy. Even though Deckard has his gun, we know that he is at the complete mercy of Roy Batty. Deckard runs like hell to save his life, not a hero thing to do.
Deckard takes a more active role than the usual detective, who is usually a POV literary device for the telling of another story. He cares about Rachael, placing the story in Thriller territory. Similar to a detective, though, is his lack of growth as a character, at the end of the film, he has not changed. The hero arc is always one of change from reluctance to acceptance and then action.
Deckard debunked as a hero? No. He never was one.