Nope, not when a perfectly healthy happy good dog is put down because the owner find it best, or when an animal shelter put down animals they can't find homes for, or when a Zoo put down young animals, because their cuteness has been expended, and the zoo doesn't want more grown animals.
In all these cases there is absolutely no reason to think the animal wants to die. So it is not about communication, it's because an animal is a thing you can own and do with what you want, as long as it isn't too cruel.