That wouldn't actually do anything. As I said, light_env lighting is calculated at compile and then that's that. There is no way to change it while running the map. There is no light being actively cast for the door to block.
The only possible way to fake it would be a ton of light_spots trying to fake sunlight, but it would look poor and you would probably run into the entity limit (since named lights stay in the map to be toggled) long before you had it looking even halfway decent. Not to mention you would be doubling the amount of data needed for the lightmaps.