Well, there are a lot of DIY Ambilight clones, most commonly running on Arduino, monitoring the colors of computer's screen and lighting LED strips accordingly.

Well, there are a lot of DIY Ambilight clones, most commonly running on Arduino, monitoring the colors of computer's screen and lighting LED strips accordingly. So it's definitely feasible. But I predict that colour changes in the page background would be a lot less pleasing and more annoying than ambient lighting changes behind the screen.