I was suspecting that Dropbox has the same automatic download limitation as Kobo store downloads. If you tap on the ... menu when looking the the files on Dropbox, you will notice the same Download all option as you will see in My Books when you tap on the ... menu there though it does not work for all items where it is permanently greyed out. You can't do this from the Dropbox item in My Books since that only shows Dropbox items that have already been downloaded and will not trigger a download of items.
Bit of testing. I had to have at least one book downloaded from Dropbox before sync showed Syncing Dropbox. Even then, no books were downloaded. I had to go to to My Dropbox and then the ... menu and download all to download the other books I dumped into Dropbox for this test.
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