Answer:
False. The driving for is the partial pressure gradient of O2 (PO2 difference), not the PCO2 gradient.
However, keep in mind that an increase in PCO2 can facilitate the unbinding of oxygen from hemoglobin. This is due to a decrease in pH associated with PCO2 increase. The H+ ions bind to hemoglobin and decrease it's affinity for oxygen, this is called the bohr effect. But the PCO2 is not the main driving force of oxygen unbinding.