I remember the announcement that an "appear offline" function is to be implemented into Battle.net. See link below:
Is it coming with patch 5.1? I haven't heard anything else about it since the original announcement on 9/20/12. I'm not playing right now, and am admittedly out of the loop on a lot of things. I probably will play again when I graduate in December. This would be a welcome addition for me. I've been hoping to have this added since RealID came into being seeing that a lot of people who see "Away" or "Busy" statuses and just ignore it.