To clarify the suggestion a little bit...
Uncheck all of the items under the Notification tab. You might want to leave the "Show status icon..." checked, it's not obvious to the user and it'll give you a little helpful information at a glance.
Under the General tab you have to have "Enable..." checked or nothing will get pushed out, and you want to have "Clients cannot change..." checked because that's what's needed to force the Notification settings to change on the client side. It takes an hour or two before the changes are seen on the client systems.