Not even then; many electronic devices (PCs, for example!) have coin-cell backup batterys or large capacitors to keep RTCs and the like running during a battery replacement (or mains power outage).
You don't actually need to transmit the data off a backup battery, just store it and ship it out once a proper power supply is reattached. (You lose the data if someone destroys their phone, but that's a much narrower range of scenarios than "turn it off, but for real".) I don't recall GPS recievers being particularly power-intensive, but there's plenty of other sensors to log, most notably the microphone.
