I just wanted to document this as I’m sure someone else will run into the problem, and there isn’t much information out there.
When you generate email from a script running on the same server, and send it to an address at the same domain, Google Apps fails to to pick it up. It picks all other email up fine.
In your Qmail config file, disable mail for mysite.com. (In Plesk, this file can be found at: /var/qmail/control/virtualdomains)
Semi-long winded answer:
Qmail handles local mail differently than outgoing mail. So if you send mail to email@example.com, from a script running at www.mysite.com, it bypasses the mail queue entirely (so Google Apps can’t pick it up), and just directly delivers it, (locally). By disabling mail handling for that domain, it’s not recognized as being a local address, and is placed into the queue., and Google can pick it up!
It’s quite simple, once you know what to do.