Can Airport Extreme be configured to work with a free dynamic DNS service?
Apple's Airport Extreme doesn't have DDNS support built in so it can't update the service itself. But it also doesn't prevent any other client from talking to the DDNS service and updating the records to point to the Airport.

You don't need to be on the router to get your public IP address; you can get get it from any client anywhere on your network that has Internet access.

The basic way DDNS works is that 


You set up a DDNS domain and account to which you will sync periodically to.
The DDNS client requests an update from the DDNS server; the client and server authenticate, and compare the IP address the client is sending with the IP address in the DNS record.
If the records are the same, nothing is done and you continue on.  If there is an update, the server updates its DNS record.
The DDNS DNS server propagates those changes throughout the Internet meaning GoDaddy's, Google's, etc. will accept the changes.
At some point, this change hits your ISP and their DNS servers so a nslookup of your IP address will return the correct domain name.


I had a router that didn't support DNS, so I created a script that ran via cron on my web dev server VM that updated it; it worked with no problem.  So, in reference to your "answer", it's your IP cameras that are doing the DDNS updates for you.