If they don't go this route, you'll likely see a condemned man struggling to hold his breath as long as he can, trying to avoid death, and eventually losing consciousness, inhaling, regaining consciousness for a moment to flail, and then dying.
I would assume that, in your scenario, the person wouldn't regain consciousness when they start breathing. They would start breathing because they had lost control sufficiently to pass out, would exhale, would inhale a quantity of oxygen-free air, and so would not improve their oxygen levels. They would continue down the path to suffocation. Continuing breathing isn't going to improve their physical state, although it will be less uncomfortable than holding their breath.