While working on a Wordpress site I was trying to connect the "Publish by E-mail" cron job while using a Google Apps email address. Here's a few tips to save you some time:

1. When setting up the Google Apps email address, make sure you pick a funky email address that won't likely be guessed (like This e-mail address is being protected from spambots. You need JavaScript enabled to view it ).
2. When connecting the login info, for the mail server make sure to use ssl://pop.gmail.com - notice the SSL tag. As well, make sure to use port 995 instead of the default 110.
3. The "From" email address should match the Admin email address if you want the email to post without approval first. This does allow multiple people to submit blogs without them being immediately published.