Nah. How many different places in the world are there with US military, Army, Navy, Marines, Air Force, Coast Guard, or Space Force(giggle) personnel? National Guard? Reserves? The National Guard has no idea which of their members are or are not vaccinated.
They will have to contact each location or outfit, determine how many unvaccinated each place has, order vaccines, get them, arrange for distribution - to ships, remote locations, etc., set up vaccination schedules, and probably a bunch of stuff I haven't even thought of. Believe me, the military doesn't work that fast. Not when EVERYTHING has to be done in triplicate. Not for hundreds of thousands of people.
I'll believe it when it happens.