Yes, many night vision (image intensification, like ANVIS) systems have high light cutoff of some type. There's an external sensor on some systems which will turn them off after a few seconds.
In addition the tubes have Bright Source Protection, but this lowers resolution, which is the main advantage of image intensification over thermal. Thermal systems just don't have the resolution, but they find heat sources better. With thermal, if a perp steals a car and then drives into a parking lot, the officers can see which cars have been running from the engines, tires, etc.
Most image intensification have Automatic Brightness Control, but this just turns the gain up and down to some degree. On my third gen. night vision scope, which uses camera lenses, the f-stop can be opened or closed. Image gets darker though when doing this, losing detail. Also, halo effect of light sources obscures vision as well. Even dim light bulbs will produce this effect.
I doubt the LEOs will use night vision for driving any real distances, and then it'd probably be rural activity, like going for a meth lab. Suddenly having two hollow tubes on your face while driving in the dark is a scary thought. Yeah, you can flip them up, but then your eyes (both of them!) are adapted to the brighter image you were getting!