Does this work as intended?
I don't know what you believe is "intended", but I wouldn't recommend using Dropbox for iTunes libraries.
First reason: every change in the library, even play count, changes the library files so you will have pretty much a constant syncing going on.
Second reason: Say you're using the same iTunes library on both computers. It looks identical on both computers. But if you change something on computer A, this change will not show up on computer B, even though the new version of the library is synced. And when you close iTunes on computer B, it will save its version, which in other words cancels out the change made in computer A. They will keep on canceling each other out.
If you're using only one computer at the time, I would recommend IDrive. You can sync the library files with a delay, so say you sync it every 60 minutes or so and you'll be rid of the problem with constant syncing.
If you're using two computers at the same time, I would very much like to know what you decide to do since I've been looking for a good solution to this for years
