Yes, smoke can damage a TV.
If it’s cigarette smoke or other types of smoking smoke, then it won’t happen anytime soon.
If it smoke from a fire, then yes, the TV is done for.
The Reason why smoke from a fire and most cigarette smoke can do damage to electronics is from the carbon it that gets released. Cigarettes release a minimal amount, and it would take years to see any effect.
Smoke from a fire can do damage to the electrical components as carbon is conductive. This will short out the leads on the circuit board and ruin the TV if it hasn’t done so already.
It’s not worth the time and effort to find if a TV survived a Fire (or restore one), and it’s better to assume it’s a goner. Some smaller electronics might make it, but things like TV’s have big vent holes which allow the carbon smoke to enter.
We live in a day and age where electronics are getting cheaper and cheaper by the moment.