From a technical standpoint, this is not something that I have tried. It may have to do with how the time machine files are actually configured. the latest backup is really a bunch of symlinks to older files that haven't changed with some new links to new files. Due to the way these are configured, you can't just copy the time machine to a new location.
In order to get this done, I think you would have to create a new base location for your dropbox sync on the NAS, then use some rsync tool to
copy the contents of time machine to the dropbox folder. I would use a subfolder inside dropbox, that way you can disable syncing that folder on your local devices.
Like the others have said, dropbox may put things in the cloud, but it may not be backup and is not the best to restore the whole system. In fact, I use cloud sync more as a way to preserve dropbox data in case it gets deleted from the cloud on accident and not the other way around. Cloud sync is also a good way to upload large files to the cloud as it will always work in the background and you don't have to have your laptop open, etc, to transfer.
Here is what I do:
1. Backup time machine to my synology.
2. Use cloud sync to backup my cloud accounts (DropBox, OneDrive, AmazonCloud)
3. Use crashplan to synology
4. Use crashplan to the cloud
Most of the files that I really need are kept on dropbox, they are synced on dropbox, but backed up using time machine and crashplan. If my laptop dies or gets stolen, I would first try to recover via time machine, if that is corrupted or missing, I'll try crashplan local and then crashplan from the cloud.
Like sfx2000 said, if you want to store a snapshot of your HD offsite, it's probably best to use Carbon Copy Cloner (it has schedules) to export to a sparsebundle every so often, but it's better to use dropbox in concert with other methods because you don't want to depend on dropbox for your only offsite archive only to find that you can't restore from it for some reason.