If we're being literal constructionists here, no, a "cannonball" would not explode. What the protagonist of that story found was technically a shell.

What's the difference? What we think of as a cannonball would generally, at least during the time period I study, be called a "shot." Cannons on ship or shore would fire shot as their main ammunition -- either cast iron solid shot sized to fit into the barrel of a gun, or more rarely stone shot approximately sized. In the Royal Navy, guns were classified according to the weight of shot they fired -- a 24 lb gun would fire, you guessed it, a 24 lb ball.

Early shells were hollow spheres filled with gunpowder, exploded by lighting an external fuse that burned into the charge. If you've ever seen the cartoon bomb with a little iron nubbin sticking out of it to hold a fuse, you've seen a representation of an early shell. The RN fired these from what were called "bomb ships," as the shells were themselves called bombs -- think of "the bombs bursting in air" during the fight for Fort McHenry. Timing the explosion was quite specialized work.

Later shells became conical, rather than spherical, and the fuse became a contact or proximity fuse, sometimes with a time delay to allow for penetration. This site has all kinds of information about shells, missiles and other things that go boom.