Sendmail does send mail immediately. Give it a few seconds at most to process the MX lookups and such, but it never takes very long. All my scripts that email use sendmail directly and when mailing to the localhost it arrives almost instantly.
It depends on how sendmail is configured on your server. If you have direct access to configure sendmail you can make it send immediately. If not, it is usually configured to queue mail for a specific period of time. I think this is the problem that mt2k is having.