If your power at home has gone out, then very likely one of these two items is also "off":

  1) your internet connection endpoint
  2) your wireless router

At which point you could not read any of the emails that an external "service" might receive for you anyway.

Plus, as another poster already stated, email servers retry several times to deliver a message (as required by the spec), so the email just waits in the senders queue until your power is back, and then arrives, a few hours late.