No, as it has no signal. Transmission towers have multiple antennas responsible for tracking the phone's signal, and with most phones being equipped with GPS chips, they only need to be turned ON to determine your location in real time.
However, an article by The Washington Post from September 2004 says a new NSA technique enabled the agency to find cellphones even when they were turned off! JSOC troops called this “The Find".
From Kdvr.com, new technology is turning cameras and smartphones into tracking devices that are capable of following a customer’s movements inside a store right down to where they’re looking. Find out more here.