Turning off notifications only does what it says, data is still transmitting.
I'm assuming OP means one of two things. Either he just wants notifications off which can be done individually in the Notification Center or all at once via Do Not Disturb toggle, or he's worried about the actual security of the network. I don't have Facebook so I'm not sure about it, but there must some kind of setting that disables push updates. And I don't believe banking apps use account sync much.