The good old boys that are members of my gun club wouldn't suggest shooting it out unless the ball was seated at the breech. But then, we have access to steel range rods, assorted solvents to soften fouling at the obstruction, and suitable hammers to gently seat the stuck ball at the breech.
While shooting out the obstruction may ar may not ring the barrel, there is no need to take that chance. I did, inadvertently, shoot a short started ball out of my 1 1/8" 45 caliber rifle with no ill effect. Still, I don't recommend such practice. Yes, I have read the article by the Bevel Brothers in "Muzzle Blasts" and in their tests they did ring any barrels. For me and by my recommendation, don't shoot out a stuck ball unless it is seated on the powder charge.