Double barrel shotguns were very frequently used, particularly by mounted men, but also some infantry. They were often brought from home. There are images and pictures of some that were contrived to use a bayonet. They offered two shots instead of one. These were, however, civilian arms, and so the locks and other critical parts were not built to the same level of robustness as a military arm, even a smooth-bore musket, which after all, is a type of shotgun, really.
A buck and ball cartridge offers a single .65 ball and 3x .310 buckshot for four projectiles. A buckshot load of the day was often 9x or 12x .310 balls. Certainly devastating at close range. In police and civilian use the shotgun developed a reputation as a fight stopping weapon. But at longer ranges, particularly with older types of non-buffered shot, the shot pellets leave the barrel distorted from contact with other shot, and since they are nominally round, they lose velocity very quickly. The spread of shot is not so wide as is often portrayed or thought of in uninformed popular culture, but at a distance of 35 to 40 yards out to 50 and 65 yards, which is easily still smooth-bore musket range, the spread of pellets starts to become so wide that the chances of achieving a disabling hit diminish.
In cases of shooting at rifle armed troops at ranges over that of a typical musket, anyone with a shotgun suffered the same disadvantages as someone armed with a smooth-bore. During the American Revolutionary War, there was actually a proposal to arm Continental cavalry with blunderbusses! The idea here was that it would be easier to reload than a conventional carbine or even brace of pistols. The flared muzzle did not spread out the shot, but it made loading from a lurching stage coach or carriage, or on the rolling deck of a ship, much easier.