The US military used to have a policy:
Don’t ask don’t tell....
Its absolute idiocracy that the FAA has any say in a vaccine situation.
If its approved by an ICAO member State’s local health organization then its fine.
They have no need to know.
Only reason they have not “approved” its use is because its not available in the USA.
I would have taken the Russian or the Chinese vaccin just as happily.