Well the function that sends the emails is residing in components/com_comment/classes/joomlacomment/josc_notification.php
notifyMailList. Look at line 335:
if (JUTility::sendMail($mailer->From, $mailer->FromName, $mail, $subject, $message, true, $mailer->cc, $mailer->bcc, $mailer->attachment, $mailer->ReplyTo, $mailer->FromName )) {
As I said we use the standard joomla function.
Perhaps what you could do is to make a var_dump before this function and watch the result:
var_dump (JUTility::sendMail($mailer->From, $mailer->FromName, $mail, $subject, $message, true, $mailer->cc, $mailer->bcc, $mailer->attachment, $mailer->ReplyTo, $mailer->FromName )) ;
Now when you publish a comment you should see an error message and the form for comment should be filled with the error message. If no error message is shown this would mean that this function is not called and this could be only the case if you have selected to disable email notifications in backend.
Since you said that it is not that important - I don't expect you to do this, but I'm interested to know what is wrong