Hmmm,
Ok, so this may not be the best solution, but it should work.
Create a Handler that periodically (say daily) sends an email to your email address. This handler should then set a Global Boolean to be true. It should then go to sleep for 5 minutes or so and the check the Boolean. If either the sending e-mail errors or the Global is true, then report an error.
Next, create an Attendant Profile (E-Mail) that is looking for e-mails from your system. That profile should call a handler which sets the Global Boolean to be False and then gets rid of the e-mail.
So, what should happen is that the first handler sends the e-mail (testing outbound) and sets the flag. Over the next couple of minutes, the email should be delivered and then picked up by CIC. That will trigger the profile and then run the handler which resets the flag. When the first handler goes and checks again, the flag is false, indicating all is well. If it's true, then the e-mail never got processed.
There is probably a better, or even easier, way. But that's the best I can come up with off the top of my head!
If you have multiple queues / mailboxes, you could make it more complex. Perhaps use an IP Table instead of a Global and send e-mails to each mailbox and then look to see which did / did not arrive.
HTH