TLDR: I do, they just don’t get delivered to the right inbox… If you want to avoid that, make sure you don’t use the Send email as option with non-GMail addresses in the Accounts and Import settings, as well as the Alternate Email Addresses in the general Account settings.
Before I decided to stop relying on Google’s services, I used the handy feature of linking all my email addresses to my GMail account. This was cool as Calendar invitations to events sent to my non-GMail addresses would automagically be added to my Google Calendar. Until, of course, they stopped, for no apparent reason. I suspect they wanted me to start giving my GMail address as a contact address. Since then, I stopped using Google Calendar.
However, the link between addresses remained. And it seems the redirection of emails from one address to the other has been re-instated, at least for Google Groups. I subscribe to a few Google Groups for work-related projects (note: I think it is a very bad idea for “work-related projects” to do that, surely you have a mailing list server somewhere in the company). Of course, I subscribed with my work address. Said work address
is was still linked to that GMail account. Save for a few initial emails, that work-related list was very quiet. So quiet in fact, that even the usual organisation emails for conference calls and other meetings didn’t seem to be sent there.
Well, they were sent. But GMail happily, and silently, re-routed these emails sent to a non-GMail address to my GMail inbox. The one I never check because I have other email providers, and told my contacts to send emails to these addresses (in fact, most don’t even know I have a GMail address). So I never actually received any of these emails, until right now, when I idly check my GMail inbox.
Tampering (reading, delaying, not delivering) with (snail) mail has always been an offence. Tampering with email should probably be too…
Edit (2013-04-02): Nope, deassociating my account wasn’t sufficient, mail still gets intercepted and redirected silently to the GMail inbox. Damnit Google! This is evil by carelessness!