Sleep isn't that important, it is going to be on a wall wart adapter. But it could be fun to try.
How fast is it to wake up?
I am going to use the Int0 as the trigger for when mail is hitting one of the switches inside the mailbox. But that might only be a very short impulse, and no problems if it runs without sleeping.
So what this needs to do, is to wake up when getting an impulse on the Int0, send the message, then go back to sleep.