I have an app that keeps saving files to my cusers/username/Documents location rather that to my cusers/Dropbox...../Documents location. Does that mean the files won't be backed up by Dropbox, or does Dropbox continue to scan the old location and move files from there?
After backup, those folders, and the files within them, are still accessible from the same place on your computer, while also backed up to Dropbox.
You can access those folders, which are backed up under “My PC [Your device name]”, from anywhere you use Dropbox, such as dropbox.com, the Dropbox mobile app, and the Dropbox desktop app on other computers.
Any changes or deletions you make to those folders from your computer, or in Dropbox, will be reflected in both places. The same principle should apply if a 3rd party app is involved, but your mileage may vary, depending the app you're going to use for this and the way it was designed to work.
If you find the chance to give it a go, please let me know the results here @assiaalex!