Linden Lab Official:If I do not allow a friend to see my online status in Second Life, will they still be able to see it on the website?

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If you uncheck Can see my online status for any of your friends, they will be unable to see your online status either inworld or on the Second Life website. They will still be able to send you IMs, chat with you, and send you inventory normally, however.

If you really need a communication blackout, you can put yourself in busy mode by choosing World > Set Busy. While you are in busy mode, you will automatically ignore all local chat, decline all inventory offers, and automatically send a "busy message" to anyone who IMs you.