Will depend on the filter and how it updates, often facebook mobile login page changes Ip addresses frequently. It is also very difficult to fully block facebook as a large percentage of non facebook internet usage is through one of their servers, so it is very possible that it will still work. If not you can probably sign in on a different network even a mobile hotspot and the login token should continue working on your filtered network without needing the facebook login server. Not sure if this was the question.