Can your cell phone give away your location? Yes it can. Anytime it has a power source attached it can be tracked; which means simply turning it off is not enough. If it has access to power, via a battery, as an example it can send and receive tracking data from nearby towers. Your signal can be triangulated between towers which can then identify your position whether the cell phone is in use or not. Removing the battery is the only way to eliminate this tracking; however, once you re-insert the battery, it re-registers the network and your location can once again be revealed.
Check out my book series American Rebellion Book 1 of the Revolution as well as the four other books in that series which can be seen on the left side of my blog page; and are available at Amazon.com. They are interesting fictional reading and provide a clear indication of what can happen if cvivilization and society breaks down and you are left to fend for yourself.