Unfortunately for the Troops it doesn’t work that way.
Exactly. If the FDA approves one or more of the vaccines as "safe", the military can compel service members to take them. Like it or not, there is no "I quit!" Option in the military for most service members. Commissioned officers who don't have a service obligation can resign their commission, but I don't know how fast that can go through. Retirement eligible enlisted can put in their packets, but those packets can be slow walked and I don't for a moment think the Pentagon is above being so petty that they would get a lot of career soldiers in trouble on their way out if they felt they needed to be made example of. You don't get to just put in your two weeks and that's that, it's all part of the bargain you get for signing up.
It works that way more than you know. Its not hard at all to get out of the military. I see it all the time.
I would estimate around 50% of the troops declined the vaccine. This could get interesting.