Just the wad will certainly not always burst a barrel, it normally takes a bit more weight to do so. This from tests run many years go as reported on by Burrard. Never-the-less one would certainly not want to intentionally fire another shell knowing there was a wad, or anything else, in the bore of the gun. Always better safe than sorry.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra