Let's assume it can be coded, since it's not as hard as you might expect. Are there any actual issues with the suggestion, besides potentially requiring the client to always be online to receive messages (even when playing singleplayer)?
Only problem I can see, as I stated here, is spammers or scammers being slightly harder to deal with. Should be no problem if a good ignore system is provided, or if there were to be an option to turn off cross-server whispers altogether.