I think online status is handled by the server, not the client, and if I remember right, at one point Blizzard said they had no plans to implement an "anonymous" or "privacy" mode where it would look like you were offline.
I think online status is handled by the server, not the client, and if I remember right, at one point Blizzard said they had no plans to implement an "anonymous" or "privacy" mode where it would look like you were offline.