WordPress autorespond to email

My question is not so much auto-respond, but to do something when an email is received from a registered users email.

I have a chat system on my website, and it will soon send out an email when someone posts a new message. I want users to be able to respond without having to login to the site, simply by responding to the email(or maybe sending an email to a specific address).

Either way, I would like to programmatically perform an action when WordPress receives an email. How would I go about doing this?

I use GoDaddy Managed WordPress hosting if that helps. Any help is immensley appreciated! Thanks in advance

One thought is can WordPress(or PHP) constantly query an email inbox using smtp, and delete mail as it is detected?