If you want to send an email using a smart host, I hope you understand that even the Smart Host should be running some SMTP server software like Sendmail or Postfix to relay it on internet. Even if your sendmail is relaying the mail to smart host properly and smart host is not configured properly to relay mails from outside or is not installed with some smtp server software, you will never receive any emails. I hope you have rebuild sendmail.cf using m4 macro and the correct sendmail.mc. If that is not working just add
You should have logs probably in /var/log/maillog file.