Stolen, possibly, if it is nice. Broken, definitely. The watches get broken, mostly the crystal, the bands get broken, water exposure kills them. Seriously, the life expectancy of a wrist watch in Basic is measured in days.
This is why he needs to learn to iron military rule: “Primary and Alternate”. It applies to everything.
When I did basic at Benning they took our watches away and didn't give them back until completion.
Not sure if they're still doing that.