RSS AI Zone
This has been done since the first mail program was written for unix[http://en.wikipedia.org/wiki/Mail_delivery_agent]. Every back end mail system in play today ( microsoft crap excepted ) has easy to configure and use hooks into very complex mail filtering with auto responders, spam filters, black hole utilities and fancy delivery systems like virtual users and such use . I was doing what you are talking about with sendmail/procmail almost 20 years ago that way and it’s how most automated response systems you see in email work.
You guys are talking too far up the stack IMO - hook into postfix’s rich capability for mail filters directly and call your chatbot in whatever language works for you direction from that hook.
It would take a competent unix/mailserver guy about 5 minutes to set up. ( don’t ask me, those days are far enough in the past I can’t claim competence anymore.. 
).
Security is a big risk also when you start talking all these web api to pass email through. Opening up something like this on a public port just seems like asking for trouble from spammers and hackers. Even very mature, heavily used, carefully scrutinized, secured, open source and constantly improved protocols like SMTP/IMAP, etc have serious problems that require full time attention and constant upgrades.
