Depends on the device. Some are active all the time, some can sleep and only wake up to get their position fix every hour or so. It's not exactly rocket science to adjust the programming.
And if you're stalking someone for a year, you'll have ample options to swap the device to a new one with a fresh battery.
For about the same price you can get a device with a SIM card and GPS/GLONASS and _zero_ ways to detect it.