Of course, we have no way of knowing for sure if all the countries of the world that have nuclear weapons will ever disarm completely. However, I would argue that this will not happen in the foreseeable future. If I had to bet, I would bet that it will never happen.
The reason for this is that total nuclear disarmament would require a huge leap of faith on the parts of various countries. Most countries that have nuclear weapons today have them because they feel that the weapons give them a deterrent. The weapons make them powerful and prevent enemies from attacking them. Countries will therefore only disarm if they no longer worry that another country might attack them. It is extremely unlikely that all countries with nuclear weapons will ever come to feel this way.
Moreover, it would be very hard to feel certain that all countries were abiding by the disarmament program. Thinking of the size of countries like the US, China, and Russia, it would surely be possible for any of these countries (and probably others) to have secret nuclear programs. If one country were to cheat and recreate a nuclear arsenal, it would have a tremendous advantage over other countries. It is very unlikely that all the countries of the world will ever trust one another enough to believe that all the other countries are truly getting rid of nuclear weapons permanently.
For these reasons, I am highly skeptical about the possibility of complete nuclear disarmament.