User email verification link
Yes, hook_mail_alter() enables you to alter any email messages sent out from hook_mail() if you know the specific key associated with the email. In this case, the key is user_register_no_approval_required. From that point, all you have to do is parse the email message body for the relevant URL and save it to your desired location.

function MYMODULE_mail_alter(&amp;$message) {
  if($message['id'] == 'user_register_no_approval_required') {
    //@TODO: Parse $message['body'] for email verification link and save it
  }
}