There's often a difference between an online friend and an offline friend. There doesn't have to be, but I bet most MMO gamers know what it's like to appreciate another player as groupmate but not want to give that person an email address.
Why not give players an option to be emailed group invitations by other players?
For example: I'm offline, but I've enabled this option. You and I grouped for the first time last night, and you enjoyed my company in the game. You're in the game now, you can see that I'm offline, but you're hoping I'll be able to group sometime before you log off. So you select an in-game option to email an invitation to me without need of knowing my email address. Just as "/tell [name] [message]" only requires that you know my character's name, this only requires the character name and my selection of "enable invitations by email".
The value of such a feature is simple. Sometimes, you may be doing something other than playing the MMO, but you're available and would log in if you had a group waiting for you when you did. You can be notified of friends logging in (only at the friends' discretion) without needing to fill your time with boring actions in the game. Such notifications would be more common if they didn't require sharing personal information.