It would all depend on if the patch will stay on the ball until it leaves the barrel. Patches work in a muzzleloader, but amuzzleloader is a constant surface all the way from breech to muzzle. In a shotgun, the patched round ball would have to exit the shell after opening the crimp, clear the chamber, travel down the barrel to the forcing cone, after that it has to travel to, and through the choke.
I have no basis as to whether or not it will work or not. If a problem arises, it would most likely be in the area of the chamber. The only real problem would be if the ball sheds the patch in the barrel. It don't see why it would be unsafe to test. Load up a few, fire one, and check the bore. And repeat.
I looked at my shotgun barrels and the end of the chamber appears to be a lip, or a very sharp angle. If something causesnthe patch to shed, that would be the most likely suspect. It could be mitigated by using the longest hull your shotgun will chamber to reduce the free bore.
This is all theoretical.