Skype for Business (Lync) 2016 does not enable the “Appear Offline” mode by default.
A quick registry fix will update the options…

Command Prompt (Run as Administrator)

Reg Add "HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Office\16.0\Lync" /V "EnableAppearOffline" /D 1 /T REG_DWORD /F