Is it possible to add the uploader shortcode to a static block? I would love to add the uploader to a certain part of my site that only uses static blocks and not pages
By saying static block you mean widget area right?
For this you can try using rtMedia Pro Sidebar uploader widget. For more details you can refer documentation here -> http://docs.rtcamp.com/rtmedia/addons/rtmedia-pro/features/sidebar-widgets/uploaders/