I'd say you're on to something with the idea of printing or embossing a repeating pattern, probably for wallpaper, see figure 8 on
this page these cylinders seem to be popular items to make into
lamps.
Justin, if you will notice it has bars rather than wires (something I've never seen on a barrel organ), those bars run on a diagonal, making it essentially impossible for them to operate a note in any sensible way, and there is no gear on the end, as would be common to an organ barrel. Not to mention the bizarre pattern and infilled shapes. To be honest, it doesn't look much like an organ barrel, even on casual inspection.
Cheers,
Roger