It depends on which setting you choose in preferences. If you picked copy that means the dropbox folder is a copy of the music in your main music folder. If you chose move, the dropbox folder contains the music you decided to upload and is only there on your computer, aside from dropbox.
By default anything you update gets changed to the database file in the cloud, but also the music track if you chose to upload it.
There is always a copy of your music that got uploaded on your computer. You aren't "streaming" from Dropbox. Just storing it in the cloud.
For backing up it's best to use the internal backup feature. Yes it takes a lot of space but I personally find it a bit safer than what you are suggesting.