I don’t think this is quite right. Read up on “time of useful consciousness”. I think if you exhale the air in your lungs and inhale oxygen-free air you’ll be out much faster than if you just held your breath. I’m not entirely sure if total pressure matters or partial pressure matters, but I’m quite sure that there will be some similar effect. I have found some claims that the partial pressure is the major factor, so breathing pure nitrogen seems like it would incapacitate someone faster than holding their breath does, because the nitrogen is actively removing oxygen from their blood.