In the most reductive and simplest of answers, yes, they do. However, much has been made of screen burn and OLED TV degradation - basically to the point of gross exaggeration and misrepresentation. And those two factors are important to separate. The latter (degradation) will happen naturally just through the effects of old Father Time - with each diode emitting its own light, this will fade ever so slightly over time. The former, screen burn, is a potential factor to be aware of but in real terms is easy to avoid.
You'll still get thousands and thousands and thousands of hours out of one of the best OLED TVs, so whenever these concerns are thrown around, they are usually just things to be aware of.