It would be an interesting idea, but the feeling I get is that from what you're saying, the look of the map would be based on your computer's clock. Now, forgive me if I'm wrong, but that's just what I'm getting from this. I think that it would work best if the look was chosen at random each time a game was started.
So, one time, you might get a game on SR where it's early morning, and the sun is just rising.
Then, the next time, it might be in the dead of night, with lanterns strung around the map to illuminate the area.
Then, in a third game, it's afternoon, and the orange hue of the afternoon sun permeates throughout the Rift.
But I like the idea, I really do! I've also had thoughts of alternate 5V5 maps that have the same idea of SR, but a unique look that might tie in with future Lore events.