It does. I have a Subaru with a head unit that stays powered on, and it has ran itself down more frequently than any other car I've had. The explanation I got from the dealer was that the residual drain on the battery is much higher, so there's less capacity to start the car. I keep a lithium ion jump starter charged and in the car, and I've had to use it a few times. If you can keep each and every OTHER draw on the battery down, it's fine.
The biggest thing that helped was realizing that the battery dies when the key fob was hung up with our other keys. Coincidentally, this was exactly the right distance for the car to constantly wake and sleep itself as it thought the key fob was entering and leaving its vicinity. Between adequate key fob faraday cages, making sure the interior lights are in the automatic or off position, and making sure all the doors are closed we haven't had a dead battery in a while.
