Unfortunately not. Dropbox is a file sharing service rather than a regular web host.
If you uploaded an image to Dropbox, you'd need to be able to just view the image on its own but Dropbox wraps the image within its own 'download this image' web page and it is not possible to just view the image in isolation.

Other than hosting the images on your own web site, you could use a Flickr account as a source of images for a Juicebox gallery. You could upload your images to a Flickr account and then select which images you want to display via Juicebox's Flickr options (see the Lite and Flickr Pro sections in the Config Options page).