Can a doctor tell if a patient has passed out if not hooked up to monitors?

No: "Monitors" don't tell us whether or not a patient is "passed out". Looking across the room at a normal but non-moving patient, we can't tell she has passed out. She could be sleeping and having nice dreams. We need to see or hear more of the patient, just as any other observer would need, in order to say whether the patient is sleeping or passed out.