A reasonable first cut might be making the local storage target configurable (if it isn't already), so that the user could point it to a file synced by Dropbox. It doesn't look like there's any daemon involved, so changes made from one box would be visible on the others as soon as Dropbox finished syncing them.
Perfect idea, simple and elegant.
Though I wonder if there would not be lock conflicts between the file-syncing dropbox does and the file-reading that stash would need.
