Postfix has the feature always_bcc. This parameter specifies an optional address that receives a copy of each message that enters the Postfix system, not including bounces that are generated locally.
Here is a link:
Search for always_bcc.
This should offer some clue as to what Postfix is doing and if it is working, though you may not want it on for too long.
The same page offers logging info. There may be an option there too, though I think the always_bcc might be more convenient than looking at a log file.
One thing I used to do as a webhost, was use a Microsoft Exchange server between all of the SMTP servers and the POP/SMTP anti-spam/anti-virus gateway. This allowed me to capture and archive every e-mail sent or received. I did this for recovery and debugging. I was able to not only backup all e-mails in one location, but also instantly recover any e-mail that may have failed and fix the situation and resend. I mention this because you may want to think about something like this at least for a period.
Perhaps the always_bcc will give you the same option. If not look at logging.
As far as knowing if your MTA is working, do what I do. Send an e-mail to a friend when they are on the phone and have them send a reply. It only takes a minute or two and if you continue to need your friend, he/she are already on the phone. Sometimes the simplist solution is the best.