I had a bit of trouble figuring out how to set up the mailbox in google apps to work with Discourse so that there is a user-friendly incoming email address for each category. Here are some screenshots that show how I did it. Tested and it seems to be working well.
In summary: assuming the domain name is foo.com, there’s an email mailbox firstname.lastname@example.org for handling all discourse-bound mail, using email@example.com to handle matching replies to topics and aliases for the mailbox to handle incoming mail for eg categoryname matched with nice email address firstname.lastname@example.org.
Google Apps settings from "Manage this Domain"
Discourse email settings
Discourse category settings