At the moment, you can only set the Query Thumbnail with one condition, for example: display the latest Version linked to the Entity as the thumbnail or display the latest Version linked to the Entity submitted under a particular Pipeline Step. You cannot say: display the latest Version submitted by a department, and if there is no Version submitted by that department then just display the latest Version linked to that Entity.
Please click 'me too' if you'd like to see if statements supported in the Query thumbnails.