A person can certainly be conscious, but can they also be not-conscious? I think that most of our cognitive time is spent in activities that don't require consciousness and consciousness itself isn't needed for the majority of activities that people do. I would go so far as the a non-trivial part of people's time is spent in a not-conscious state.
That doesn't jive with normal definitions of consciousness. The word we use for "not-conscious" humans is "unconscious".
Amusingly, I think Ted Chiang actually wrote a short story about this very concept (it involves people committing a form of suicide that removes their conscious experience but they still act and live in society as some kind of psychic zombie. I’m pretty sure it was him anyway, can’t recall the story name