When the game is down or when we simply just can't enter the game, it would still be nice to be available to receive and send mail using the Mail system. The updates wall is fine but sometimes you just want to read old mail or send mail directly to someone in-game. Could a Mail or Inbox link be added to the Home page?
If the issue is attachments and inventory, I think it's perfectly reasonable to exclude it from offline Mail or prevent the player from accessing it while not in-game.