How can I render a field inside a tpl.php that is hidden on the UI
You can add any markup or additional fields to the node teaser view or node full view using hook_node_view().
The following example is adding a taxonomy name to the teaser view.

function MYMODULE_node_view($node, $view_mode = 'full', $langcode = NULL) {
    if($view_mode == 'teaser'){
     $tname = db_query('SELECT name FROM {taxonomy_term_data} t WHERE tid = :tid', array(':tid'=&gt;$node-&gt;field_category['und'][0]['tid']))-&gt;fetchField();     
     $node-&gt;content['my_taxonomy'] = array(     
        '#markup' =&gt; '&lt;div&gt;'.$tname.'&lt;/div&gt;', 
        '#weight' =&gt; 10, 
      );
    }   
}


You would not need to update node.tpl.php.