Appearing offline will show you as offline to everyone in your Blizzard friends list. Once you have joined a game, the experience of appearing offline might be slightly different depending on which game you are playing. In the case of World of Warcraft, your guildmates will see your character come online and enter WoW’s in-game chat channels, and anyone who has you as a character-level friend will see you online on their friends list. Everyone outside of the same game as you will not see you online or playing any games.
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