If a block variable exists but renders nothing, a link to <block> is returned

e.g. Note the addition of

elseif ($variables['path'] == '<block>') {
		return; //No need to display a link to http://yoursite.com/<block>
	}

function menu_attach_block_link(&$variables) {
  $block = FALSE;
  $options = $variables['options'];

  if (isset($options['menu_attach_block']) && !empty($options['menu_attach_block']['name'])) {
    $block = menu_attach_block_load_from_key($options['menu_attach_block']['name']);
  }

  // Render a block if one is attached to this link.
  if ($block) {
    $link = '';
    // Render the link with the block content afterwards.
    if ($variables['path'] != '<block>') {
      // Build the link manually instead of using l() to avoid getting caught in
      // theme_link() again.
      $link = '<a href="' . check_plain(url($variables['path'], $variables['options'])) . '"' . drupal_attributes($variables['options']['attributes']) . '>' . ($variables['options']['html'] ? $variables['text'] : check_plain($variables['text'])) . '</a>';
      $attributes = array(
        'class' => 'menu-attach-block-drop-link',
        'id' => $variables['path'] . '-drop-link-' . $variables['options']['menu_attach_block']['mlid'],
      );
      // Pass a space as the fragment parameter to get a <a href='# '> link.
      // @link http://bit.ly/zZXArS @endlink
      $l_options = array(
        'fragment' => ' ',
        'external' => TRUE,
        'attributes' => $attributes,
      );
      $link .= PHP_EOL . l(t('More'), '', $l_options);
    }
    // Get the block html.
    $block_output = menu_attach_block_block_render($block['module'], $block['delta']);
    if (!empty($block_output)) {

      $variables = array(
        'orientation' => $options['menu_attach_block']['orientation'],
        'content' => $block_output,
      );
      $block_output = theme('menu_attach_block_wrapper', $variables);
      return $link . $block_output;
    } elseif ($variables['path'] == '<block>') {
		return; //No need to display a link to http://yoursite.com/<block>
	}
  }

  // Otherwise, pass through to the original theme function.
  return theme('menu_attach_block_link_default', $variables);
}