For the moment the short answer seems to be 'no'.
Fit bit have a detailed article on their website about how their SPO2 monitor works. It starts off with this statement:
"The Fitbit SpO2 feature is intended for general wellness purposes only and should not be used or relied on for any medical purposes. Consult your health care professional about any questions or health issues you may have".
Personally, I have a Fit-Bit and use it to help monitor the issues I have with sleep-apnea, as a guide.
However, I wouldn't use it for something important.
In the future, I expect that these devices will be improved and approved by the MHRA and FDA for clinical use.
Generally, we would recommend instead you buy a pulse oximeter, costing around £20, more info here: https://www.digitalhealthcoachuk.net/pulse-oximeters