How? The backup has to work properly even if all other copies of the original project are completely lost, which means it has to contain everything. From Dropbox’s point of view, the files it contains are all completely new.
If you store the live project in your Dropbox folder, then it will automatically sync to Dropbox, just as it does now. If you have set the backup location to your local drive, then yes, you would need to use “Backup To” to place a backup on Dropbox.
(I would recommend “Backup To” rather than “Save As” because it will automatically ZIP and time stamp the backup, making it easier to tell which is the backup and which is the live project.)
Again, we recommend storing either the live project or the backups in Dropbox, but not both. Dropbox errors do happen, and having a local copy will protect you in that event. If you haven’t already, please read the first post in this thread, on best practices for using Dropbox: