An interesting idea!
My general approach would be not to bother with the special email address with programmatic access. I feel it would be more logical to subscribe to the newsletter in question with my existing email, set up the Sieve filter to put these messages into a separate folder, and then write a tool that would access my mailbox via IMAP, look into that folder and update the RSS feed as needed.
But since I’m running my own mail server, I might as well just have a separate address, a Sieve filter to save the messages to a particular directory on the server’s filesystem, and have a script to pick it from there and generate the feed. This would be faster to implement, since there would be no need to figure out the whole IMAP part, but less fun (for the same reason).