The big MGS logo at the right?
What I often recommend that people do is create an exhibit and leave it unpublished. Then, they can upload their random images to it.
If you were to create a simple plugin that grabbed images from that particular exhibit you could do what you wanted. Something along these lines...
<plug:random_logo />
And the code...
function random_logo()
$OBJ =& get_instance();
$background = $OBJ->rs->fetchRecord("SELECT * FROM ndxz_media
WHERE media_ref_id = '25'
ORDER BY RAND() LIMIT 0,1");
return "<img src='" . BASEURL . "/files/$background[media_file]' />";
25 is made up - that should be whatever the 'id' is of the unpublished exhibit.
I am sure this needs more work but give it a try and we'll walk you through the rest.
;)