PHP to show if content has new comments in taxonomy-term.tpl.php?
Yes you can but it will it performance without proper caching. Don't do that in tpl because you can cache it, even with page cache.
Code look something like that using drupal api.

&lt;?php
$has_comment = false;    
$nids taxonomy_select_nodes($term-&gt;tid);
foreach($nids as $nid){
$node = node_load();
  if($node-&gt;comment_count &gt; 0){
    $has_comment = true;
  }
}