According to Hatcher*, the US Ordnance Department did a bunch of experiments on this and found that stuck cleaning rods and patches and "hatcord" cleaning devices and even bullets could readily be removed from the Springfield rifle by firing a case half-full of the regular (not blank**) powder with no bullet.
However, it was decided that since the experiments were done in carefully controlled conditions, and there was no way to predict what conditions there might be in field use, it was not a method to be recommended.
He also notes that several times during the experiments with really bad obstructions, the firing pin went click and nothing happened. They had plenty of fun opening the bolts by tapping them open with a broomstick, where the bolt suddenly flew open with a loud pop and one case was ejected so smartly that it got stuck in the opposite wall.
Hatcher comments extensively on several anecdotes (as opposed to rigorous experimentation) where bullets have been shot out of barrels. In most instance, the barrel lets go. However he also notes that one machine gun had developed a distinct bulge at the point where the following bullet hit the stuck bullet, went on through, and left a distinct egg-shaped bulge in the barrel. The machine gun continued to operate normally.
He also notes an instance in a 1917 revolver where a person had shot five followup rounds and all six bullets ended up stuck in the barrel.
This, however, you will note, was with a revolver, where excess pressure could be relieved from the barrel-cylinder gap. When the 1917 barrel does let go, it is usually along the stamped-in lines saying "Property of U.S. Government."
All in all, a barrel with a stuck bullet or any other obstruction should be taken to a professional for removal.
* See Hatcher's Notebook, "Experiments with barrel obstructions," pp 180-197, and "The strength of military rifles," pp 198-211.
** Blank powder is extremely fast powder designed to generate standard exit pressures with no projectile. Don't mess with it.
Terry, 230RN