No. But that's a separate matter. Someone may have a sat of 100% which is due to tenuous compensation in the presence of a respiratory challenge, but noting that compensation is a clinical matter (tachypnea, etc).
Knowing that patient's PaO2 would give you a better sense for how tenuous their SpO2 truly is -- whether they have a surplus of oxygen tension or barely enough to fully saturate their hemoglobin. But again, that's not a direct factor in oxygenation status, which seemed to be the topic here. Barring a failure of the equipment or some fairly unlikely confounders, a measured SpO2 of 100% does denote normoxemia; the patient's PaO2 was one of the factors that made that happen, but that's where its contribution ends.
Actual, total oxygen DELIVERY will involve factors like hemoglobin content and cardiac output and oxygen affinity and so forth. But PaO2 doesn't really measure these either. (Well, I suppose it technically speaks to oxygen affinity when compared to the sat...)