I believe the answer to my original question is no, it is not possible (please update if Views changes to allow this).
To accomplish what I needed, I ended up creating a custom module instead of using Views. I lifted the query that Views had generated as this was essentially what I needed. After returning the nid's of the nodes in question, I have drupal theme the nodes:
theme('node', $node, $teaser, $page);
Add each themed node to an array,
$items, and then theme that array into an unordered list:
$rendered_list = theme('item_list', $items, NULL, 'ul', array());
I then set the block's content to that returned list.
$block['content'] = $rendered_list;