No, the army would never give up their pritzus for that. This is Provence so openly every time there is another report that the army forced religious mizrachi soldiers to listen to Kol Isha against their will. Is the Kol Isha helping them fight better? Of course not. It is the pritzus they wish to IMPOSE on others.
And that is why there are MULTIPLE reasons the Gedolim are dead set against frum yidden joining the army. Something we must fight with our lives against.