Having said that, Google certainly run many many mail servers, as such an outage that impacts delivery for one group of people does not necessarily impact everyone. This is the difference between robust systems and those with critical lynch pins that create system wide outages.
So the people who are supposed to do work for you also can't work?
But if everyone's email is down, they won't be able to send those messages, so they won't think we received them to ignore them.
(Then again, email is kind of uniquely bad here, because of the way SMTP works as a store-and-forward protocol. In most protocols, if my server went down, your client wouldn't be able to connect to it, so it'd be pretty clear something is wrong. With SMTP, your client can just "put a message on the Internet" for my server to receive, and won't know for 48 hours or more that my server isn't there any more.)
In fact, if total downtime is constint, I would prefer they overlap.