I'm beginning to think that mIRC simply does not attempt to respond to a DCC request if the requestor's IP address is the same as the target's IP address.
This is not correct. You can certainly DCC yourself with a properly configured mIRC. I recommend this to users all the time in order to test their router configurations. And yes, I have also seen users successfully perform intra-LAN DCC operations with mIRC too.
When you say "nothing happens", do you mean no connection attempt is even made from the target machine?