It's been two years. That is an extremely long time for a task like that.
For those asking why I would want an offline feature or to just ignore people, it's nice being on an alt where you can just game alone in privacy.
I'm really mad I never thought of this or that I wasn't told sooner, thank you sir.If you REALLY REALLY want to appear offline, it's very easy to do. All you have to do is connect to the game, then while you're on the character select screen, tell your firewall or router to block port 1119. Then log into your toon. You will be in game but if you open your friends list you'll get "battle.net is unavailable" and noone will be able to see you online. Of course, guild chat will still show you log on. And anyone that has you on the old fashioned WOW character friend list will be able to see you. But noone on battle.net will be able to.
Make sure that you keep 1119 open until you're at the character select screen. If it's blocked before then you won't be able to connect. I THINK that 1119 TCP is all you need to block. To be safe you can block UDP too.