Demon-possession is in the realm of Catholic practice. Despite the media's obsession with it, so-called "genuine" events are extremely rare in Church history. The most famous modern case (which inspired the book and film "The Exorcist") occurred more than half a century ago, in the 1940s in the United States. In my formal religious studies, it is the last major case with any recognition by the Church.
If such a thing were truly possible and such a demon-possession occurred among the Witnesses, it would cause the end of the JW religion. The reason? It would take a miracle to stop the event, and the miracle would be performed at the hands of Catholics.
Theologians are divided as to exactly why, but so-called genuine cases of demon interference seem to only get solved by Catholic exorcism. Yes, I know what you are thinking...here's a Jewish philologist stating that demons are real and only Catholics can control them, but that is not what I mean.
Reporting on what is known is that the very few supposedly genuine cases have only been successfully handled by the Catholic rite administered by proper ecclesial authority. You can believe it as a ruse invented by the Catholic Church or a lie or foolishness, but it is how things seem to work. I had to study such things in my academic studies, even investigate a haunted house as part of Demonology 101. I have no explanation for some things.
Like the case in the 1940s which began in a Lutheran household, when a case gets too hard to handle, regardless of the convictions of the "victim," in the end you call Rome. It happens among Protestants, the Orthodox, Jews, and even agnostics and a few cases I know that have involved non-religious folks: got bad juju, don't mess with it. Call a priest.
Again, in case I get misunderstood, I am not saying that such things as demons are real. I am reporting what happens in the real world with hauntings, reports of spirits, etc. that defy solution and seem to endanger people. The Catholic Church has psychologists, researchers, and of course trained priests to investigate things such as this, and frankly they are the only ones who seem at ready to deal with the unknown cases which don't fit common explanation.
If ever someone among the JWs got possessed, and I mean in ways that defied enough doctors and scientists that people started calling the local Catholic bishop, that would change a lot of minds really quick. The Church will not lightly accept any case either. If they get involved it is because explanations have failed and real physical danger exists.
If the exorcism is successful, then what? Disfellowship the person for being miraculously saved by events that disprove JW theology? Deny that something happened through the hands of a Catholic priest? Continue as a JW despite everything you saw with your own eyes?
For Catholics to determine actual possession that requires the rite of exorcism is more vigorous than a two witness rule, however. They employ scientific and medical methods to ensure that no other explanation exists before the rite is performed. Psychologists and other medical professionals weigh heavily in the investigation process.
As for myself, despite my personal convictions as a Jew, if ever these became defied by phenomenon of a nature that could not be explained and seemed like I was being attacked by devils, I wouldn't bother calling my neighborhood JW, the Pentecostals that live next door, or even my rabbi. If I started cursing G-d in Latin and spinning my head around, call a Catholic priest. Damn whatever I believe.