Yes, putting your database in the Documents directory will do exactly what you want: allow back up to iCloud without syncing to iCloud.
Syncing requires moving to the ubiquity container, but thats not what you want.
More information can be found in the Apple Technical Note which explains how to exclude a file from backup. Of course, for the backup to work, the user has to have set up their device to back up to iCloud.
Edit: Here is another helpful link: Apple's App Backup Best Practices section of the iOS App Programming Guide.