Appear Offline is a feature that many players have requested and that has been on the back-burner for over three years. 

Jeff Kaplan clears the air. 

We would like to add an "Appear Offline" option to Overwatch. We are in the process of coordinating this with Battle.net and the other game teams. Because our social system is a cross-game system (WoW, Hearthstone, Heroes, SC2, D3) adding this functionality is not trivial for us. I know there has been discussion around this feature for a long time, and things have definitely not moved at a rate which is acceptable, I can assure you we care about the feature and want to figure out how to make it happen.

Thanks Jeff!