Unfortunately this does not seem to be the case:
Dropbox saves deleted and previous versions of files for a specific period of time so you can recover them if desired. After that time, the deleted files are marked for permanent deletion in our system and are purged from our storage servers. Once they’ve been permanently deleted, they can no longer be recovered or restored.
Your default file recovery period depends on your Dropbox plan:
- Dropbox Basic, Plus, and Family users have 30 days.
- Dropbox Professional and Business users have 180 days.