I know that a "desk mode" can be triggered with a magnet. I'm sure it has a software car mode since it's a part of stock Android, but I'm not sure if there's a way to trigger it with a magnet or NFC tag, and there's no stock app that would launch when entering car mode.
Even if you could trigger it with a dock and automatically launch a car mode UI, Google has drastically reduced the usefulness of this in recent versions of Android, since tapping the Home button while in car mode no longer returns you to the car mode UI - it returns you to your normal home screen instead.
That said, I'm with Clementine_3 - I use Touchless Controls in the car, and haven't missed car mode at all.