Thanks for using Side by Side.
Yes, you can save Dropbox images to Side by Side. Just go to Dropbox in a web browser window, log in, and navigate to the folder with images. Tap the image, and then the star button in the browser, and save the file.
You can also use batch download mode to quickly save many images from a dropbox folder. The batch download mode can also be found inside the star button in the browser window.