I know how to do it on the android I have so if I dont open up facebook or any other app there is no way in the world that any incoming notification nor attempt of data will be use unless I hit on the icon. Still, no idea how to do that on my iphone.
There is no real way to do this on the iphone. The only for sure way is to Turn off data. Settings -> General -> Network -> Cellular Data
To try to do what you are asking I would try the following with no promises:
-You can make sure that any data using app is not in the notification, this includes any badges that appear on the icon
-Ensure mail is set to Fetch Manually
-Ensure iCloud settings is not using any data
-Ensure photostream is not using any data