Will they or will they not have a say?
Of course they won’t have a say. They never do! That is the price of enlistment.
...I would bet that our troops would have NO say in this matter....! just as when I was in the military, every year we had to get our flu shot - whether we wanted one or not, whether we believed in the effectiveness of this shot or not, you got your shot, or else.....unless there was a very VERY good and substantiated reason why you could not get this flu shot, I believe an Article 15 awaited you if you refused it.
About as much say as I had with the Anthrax vaccine and boosters, which probably shattered my immune system so that i am allergic to the world now.