I think there is a difference between "Turn chat off" and "Sign out". Correct me if I am wrong in my perception:
Turn chat off -- This option will not sign me out, instead it will not show me people who are online. I do not want that.
Settings-->Disable Notifications -- This option will "Mute" the incoming messages for me, however person sending me the message will still find me Online!!
I wanted to know if there is any option to sign me out instead of disabling incoming messages/hiding people who are currently online.