Yes, sleeping with the tv on will be bad for your eyes because there is the radiation from the tv. The screen is too bright which will affect your sleeping quality too. You should not do this. Although you close your eyes, the radiation from the tv may hurt the surface of the eyes skin.
Well, I quite understand your assumption, because during Saturday nights, we tend to watch TV shows in the couch to sleep. And we usually forget to turn off the TV. So, yes of course, it would have an amount of damage to our eyes because the TV gives out some harmful lights to our eyes. So, I suggest that you pre-set the time of closing so as to better protect your eyes.
It is bad to your eyes with TV on, when sleeping. Especially for children, sleeping with light on in their room have an increased chance of near sightedness, so does adults. People need the hours of darkness for their eyes to relax their opening eyes. Falling asleep with the TV for a long time, your eyes would be hurt.