The default block handler doesn't support configurable items, but extended block handlers might be able to do interesting stuff with it.
public function executeHookBlockList($delta = 0, $edit = array()) {
$delta = $this->view->storage
->get('name') . '-' . $this->display['id'];
$desc = $this
->getOption('block_description');
if (empty($desc)) {
if ($this->display['display_title'] == $this->definition['title']) {
$desc = t('View: !view', array(
'!view' => $this->view->storage
->getHumanName(),
));
}
else {
$desc = t('View: !view: !display', array(
'!view' => $this->view->storage
->getHumanName(),
'!display' => $this->display['display_title'],
));
}
}
return array(
$delta => array(
'info' => $desc,
'cache' => $this
->getCacheType(),
),
);
}