No, it will not. If you connect it to your 12V cigarette lighter port, it’ll turn on/off with your car. However, if your car provides constant power through the 12V port even when your vehicle is off, please make sure that you unplug it when you exit your vehicle to prevent this from happening.
If you decide to hardwire the camera to your vehicle via your Type S Hardwiring Kit (AC533513, sold separately), you’re still in good hands; the hardwiring kit will automatically stop drawing power from the battery if it detects that your battery level is low.