I don't think Linden Lab would want to be sending messages that say you're offline when you're not.
Maybe it would be better to modify busy mode and have it send a message like:
"The user is currently busy. Your message has been sent to their email address"
The current 'Busy' mode sends a user defined message already. But when in busy mode, we can't hear the chat from the avatars around us and instant messages still arrive. This isn't really much use because sometimes I'm actually just busy chatting one to one.
I find it really frustrating to be trying to chat (avatar to avatar) and have some control freak in IM mode whining at me for not responding. Believe me, I've had this on quite a few occasions. Some people will take it very personal if you don't respond quick enough.
In the real world we can turn our cell phones off. Why the hell don't we have this option here?.
It reeeeeeally pisses me off!.
I sometimes think it's down to social engineering from Linden Lab, or rather - Phil the closet sociologist. Yet I would actually be more sociable if I could disable IM mode. Right now I'm afraid to chat with people because of the flood of IM's that often follow the next day. Then followed by several days of gently trying to tell my new friends to piss off and stop IM'ing me.
Don't get me wrong. I love people, but hell, I can't talk to everybody in SL at once!
I feel socially stifled when in Second Life.
To sum up:
The more "friends" you have, the more instant messages you get.
Instant Message Mode=Bad!
Okay, I'm off to breathe into a paper bag now. Byeee! 