Often times, especially for fired artillery, if you know the battle then you can narrow down to a large degree where it might have been found. A large moving battle like Shiloh or Gettysburg can be tough to do that at but a smaller one like Kennesaw Mountain isn't. Once you know the caliber you can figure the type of cannon and often narrow it down to a few batteries and then just go locate the impact area. It still is a long shot that you'll find anything but helps the odds a lot if you are obsessed with finding a particular round. But most of the time people just prefer not to say or give vague answers.
Regarding this item, in my opinion, it appears more period than war used much like a 3.67-inch Delafield and thus only of interest to advanced artillery collectors. But for the advance collector it is apparently a very hard item to add to the collection.