Not the answer you're looking for, but Mandrill doesn't let you do this. The only way of checking if an email has been delivered is to poll Mandrill (with the message/info.json API). To see if the message is delivered you have to check the smtp_events
and look for an event with diag
starting with 250. As you've already experienced it may take a long time between delivery and when a message is accessible through the API. In my experience the normal case is around 10 minutes, but it might take many, many hours (this is the case for bounced emails as well as emails that got delivered immediately).
If it is important to you to know when an email is delivered, I would recommend you to switch to another email provider. There are plenty of different ones out there. I've personally used Amazon SES. They're cheaper than Mandrill, and you can expect a delivery notification after a second or so. Do note that Amazon SES is a bit more bare-bone than Mandrill (they don't have support for open/click-tracking, templating, dedicated IP, etc.), so it might not be the right provider for you.