Hi Sean,
No, you cannot use shortcodes in those boxes but you can add the shortcodes to the template directly. Note, you must be using the Default Events Template in Events > Settings > Template. Make a copy of /wp-content/plugins/the-events-calendar/views/ecp-page-template.php and place in an ‘events’ folder in your theme. Then, open up the file and you’ll see the function calls to tribe_events_before_html() and tribe_events_after_html(). Then just execute the do_shortcode() (http://codex.wordpress.org/Function_Reference/do_shortcode) function wherever you want:
echo do_shortcode('[adrotate block="4"]');
That should work but let me know if you need anything else.
Regards,
Jonah