Yes. Pull the battery and the SIM card, and your phone is an inert piece of hardware. It ain't talkin' with nothing!
Without the phone to sync with, no more Fitbit data or run tracking can be uploaded to the Cloud, as Fitbit uses Bluetooth to connect to the phone at short ranges (20 feet or less) - meaning that a Fitbit can't ping off of a cell tower or communicate with a GPS satellite (via an incoming signal the phone uses to figure out where it is - e.g geolocate) on its own. Also, if you lock a phone in a cookie tin can or an ammo can - any heavy metal box or maybe even a Mylar potato chip bag (e.g. a Faraday cage) that should also block any incoming/outgoing signals to/from a cellphone. If in doubt, then go to work with a hammer on the phone (and his little friend Fitbit too) after pulling the battery and SIM card from the phone, wrap the pieces in a roll of aluminum foil folds, bake at 325 degrees for several hours, and hide the phone remains at the bottom of a coal mine! Let NSA find that!
I read recently that Apple is developing hardware driven Technology that will allow not yet released Iphones to call 911 (and, presumably, maybe be able to geolocate via GPS satellite info, and MAYBE allow Apple to ping a "dead" phone's location) if the phone has no battery (for you technerds out there, the article did not say how - maybe a capacitor?). But this Tech is still down the road.
I hope this helps.
MOO