If you use the option to appear offline and then log into the game, do you also appear offline to your battle.net friends?
If you are only friends through Battle Net and not via the in-game friends list, then you would show as offline on their end.
But should they add your character(s) to their in-game friends list, then they could see that character online.
EDIT: I did check this through using 2 of my Battle Net accounts. My alt account could not see this account while it is marked as offline via the App. However, the alt could see this character on her friends list in game.
On the alt character, this Battle Net account shows as offline, but Kyzera shows as online. The blue part underneath where it shows Kyzera is this Battle Net account (Bnet names are blacked out).
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I should clarify. I have a Warlock on server A. The people on my battle.net play on server B. We have added each other via battle.net app but not character name.