From http://www.facebook.com/note.php?note_id=76191543919
"Facebook generates and stores four images of different sizes, which translates to a total of 60 billion images and 1.5PB of storage."
This means that all of Facebook's photos (a massive amount of data) are stored on Facebook's servers. Your application will just move the pictures form the device to Facebook's servers. You will need no back-end server if all of the uploading is done on the device, because the pictures will go straight to Facebook's servers.