What sort of appear offline feature would make you happy?

Recently, we learned that some strings pertaining to an appear-offline feature had been added to the most recent Hearthstone build. This was good news for the Blizzard community at large, since appearing offline is a feature people have been wanting for years and years now — as well as one Blizzard has been working on for years and years.

But once the initial excitement wears off, one has to wonder what exactly these strings mean for the Blizzardsphere at large, and how exactly appearing offline would work for each individual game. For something like Hearthstone, it’s relatively simple — unless you’re randomly matched with a friend, it’ll be hard to ever know you’re online.

For something like WoW, it’s a lot more complicated, since you have an in-world character and may very likely be part of a guild. Would an appear-offline feature hide you from everyone? Or would running into people in the world mean they can tell you’re online but hidden? Would you be able to see and participate in guild chat, or would that be disabled?

Different people have different ideas as to what appearing offline ultimately means, which is why I want to open this up to you folks. What’s an acceptable form of appearing offline for you? Should you be invisible everywhere? Unable to be matched/grouped with friends? Or is simply appearing offline in the Social tab enough?

Moreover, would you be okay with some Blizzard games having this feature before others? Or would you prefer it become a Blizzard-wide service first, and then have game-specific tweaks made? Personally, I’m okay with baby steps, but I’d love to hear arguments for any and all of the above.