I'm pretty sure he's not carrying a gun. But maybe I'm wrong... Anyway, if you wanted him with a gun, why not? IMO, you're the writer, so, you can do what you want. It could be dangerously interesting...When you start writting, anything could happen
He doesn't carry a gun in the show. He's a lab tech, not a CSI. In FanFiction you can write it any way you want. But if you're following canon, then no gun.
ITA with Dreamboat; in canon, no gun, but in fanfictionland, you write the way you want. Maybe Adam got a promotion, and now works in the field? He could carry a gun then. Nothing is wrong in the world of imagination!