Should you do it . . . no.
Has it been done . . . yes.
I've seen ramrods go downrange at NSSA shoots and I've seen it done several times at small, private shoots. It's like "dry balling" a rifle when you get your attention somewhere else and forget to put a powder charge in . . . or you end up double charging. That's why it's important to keep focused on what you're doing. I've never seen any barrels damaged from it . . . but I've seen some pretty embarrassed fellas with red faces. It's best not to laugh too loudly though and you never know when the same thing could happen to you.
I'm sure that it was done many times in the Civil War during the heat of battle. Just like the muskets being loaded with more than one cartridge and the soldier forgetting to cap his weapon Years ago I read where about 25% of the muskets picked up off of the field at Gettysburg after the battle had more than one cartridge in them and if I remember correctly, one had seventeen. Under stress, anything can happen.
If a pair of '51 Navies were good enough for Billy Hickok, then a single Navy on my right hip is good enough for me . . . besides . . . I'm probably only half as good as he was anyways. Hiram's Rangers Badge #63