As the title says, Can you?...
This was very popular back then with Bungie's last game series.
Idea: Maybe it could be a emote where you can still move and look.
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Yeah, I was hanging out sitting while playing with friends, and I left to go get some soda, then when I got back and stood back up my weapon was lowered. I have no idea if it was a button I pressed or anything. My weapon didn't go back to normal until I melee'd (or shooting would work, too). It is possible, though, we just have to find out how.