Well, they’ve done the study, and the results are nothing if not surprising:

Here’s one simple way to keep your children healthy: Ban the bedroom TV.
By some estimates, half of American children have a television in their bedroom; one study of third-graders put the number at 70 percent. And a growing body of research shows strong associations between TV in the bedroom and numerous health and educational problems.
Children with bedroom TVs score lower on school tests and are more likely to have sleep problems. Having a television in the bedroom is strongly associated with being overweight and a higher risk for smoking.
One of the most obvious consequences is that the child will simply end up watching far more television — and many parents won’t even know.

I will admit that I had a television in my room when I was a teenager… of course, I figured out a way to match multiple adapters in series to run cable television on my Commodore 64, so one could argue that the unhealthy effects of the tube were somewhat counterbalanced by the encouragement of geekhood (which isn’t to deny that I finished off my teen years with a number of very unhealthy traits and habits).