Yes, the hair that has grown out of the scalp and skin is practically dead.
However, the cells that create hair inside the skin, particularly those close to the hair follicle's bulb, are very active and receive nutrition from the blood vessels.
Living thing:
Food, water, light, temperature within specific limitations, and air are essential for all living creatures.
Living things exhibit a multitude of qualities to varying degrees: they breathe, move, respond to stimuli, reproduce and develop, and are reliant on their surroundings.
Hair that has grown from the skin and scalp is effectively dead.
Regardless, hair is framed inside the skin, (hair cells) particularly close to the bulb of the hair follicle are particularly lively, and the veins offer supplements.