Wikipedia agrees with you. According to http://en.wikipedia.org/wiki/Apnea: "Blood leaving the lungs is normally fully saturated with oxygen, so hyperventilation of normal air cannot increase the amount of oxygen available."
To elaborate a little: you don't sense the oxygen level in your blood. You sense the CO2 level, using acidity sensors in your aorta. CO2 dissolved in your blood reaches an equilibrium with carbonic acid, which means that the acidity of your blood is proportional to the amount of CO2. It's stuff like this that makes physiology fun to study.