Agarza has answered your main question by saying “Jehovah's Witnesses (anointed or otherwise) are not immune to demonic possession.” They acknowledge that nobody is immune from attacks by demons, whether they are Jehovah’s Witnesses or not. Clearly, prevention is better than cure, as this extract from an article on demon possession from ‘Insight on the Scriptures’ shows:
Often the wild and uncontrolled conduct of mentally unbalanced persons is due to possession by these invisible minions of Satan. Sometimes it is reported that spirit mediums have cast these demons out; this calls to mind what Jesus said: “Many will say to me in that day, ‘Lord, Lord, did we not . . . expel demons in your name . . . ?’ And yet then I will confess to them: I never knew you!” (Mt 7:22, 23) Compelling reasons, then, for heeding the counsel, “Be watchful,” and, “Put on the complete suit of armor from God that you may be able to stand firm against the machinations of the Devil” and his demons. Source: https://wol.jw.org/en/wol/d/r1/lp-e/1200001154
Your secondary question asks: Would only Holy Spirit anointed JWs be qualified to do what Jesus did – cast devils out of people by the Spirit of God? Here are a couple of quotes from the official Jehovah’s Witness website. Please note that all emphases are mine:
Should Christians Practice Exorcism? True, during the infancy of the Christian congregation, Jehovah God often enabled Jesus’ disciples to perform miracles under the power of His holy spirit. But such miraculous gifts of the spirit were no longer needed once it had been proved that the “hand of Jehovah” was with the followers of Jesus Christ. (Acts 11:21) Consequently, the miraculous gifts of the spirit and unusual demonstrations of its power passed away.—1 Cor. 13:8-13.
While there is no Scriptural authority for exorcism ritual today and true Christians do not practice it, that does not mean that godly persons have no protection from wicked spirit forces. They do, indeed, have all the help that is needed.
Of vital importance is faith in Jehovah and earnest prayer to him. If under demon assault, it is essential to pray to Jehovah God through Jesus Christ, using the Divine Name. “The name of Jehovah is a strong tower. Into it the righteous runs and is given protection.” (Prov. 18:10; Phil. 4:6, 7) Appointed overseers in the Christian congregation gladly have assisted those desiring to serve God but who were being troubled by the demons. Yet, the mental attitude of the individual himself is of importance. It is vital to resist wicked spirit forces, and this is effective. “Oppose the Devil,” wrote the disciple James, “and he will flee from you.”—Jas. 4:7.
Modern-day exorcism with its ritual is not the answer to demon possession. Rather, Jehovah God has lovingly provided protection from wicked spirit forces, and prudent persons will avail themselves of it. No, Christians should not practice exorcism rites. But they should keep their minds and hearts fixed on the worship and service of their heavenly Father. Source: 22 May 1977 Awake! https://wol.jw.org/en/wol/d/r1/lp-e/101977370#h=1:0-30:357
I know from first-hand experience that when demonic forces are at work, praying to God in the name of Jesus Christ is effective. 45 years ago, while on a residential training course, some of my colleagues set up an Ouija board and started to ask questions. To their surprise, they got answers. Most were sceptical, but one young man became possessed. He started speaking in a voice not his own. He started using vile language. He collapsed and was taken to his room where someone with basic medical training monitored his vital life symptoms. While that was going on, I went to the pay-phone, looked up the telephone directory and found a list of Catholic residences. I started to phone for a priest, determined to drag someone over to give spiritual help. Before I got an answer, the young man in question came round, and his pulse/heart rate returned to normal. He had no idea of what had happened to him. Eventually, we were able to retire to our rooms.
During the hours of darkness, I woke up suddenly, aware of something in my room. There was nothing to see and there was no sound, but I could smell the fear on me. I sensed the presence of evil, and no, I was not under the influence of alcohol, drugs or other substances. I cried out to God to protect me and called upon the name of Jesus Christ. It was probably the most heart-felt prayer I ever made. That evil presence left.
Next morning, the caretaker said both his dogs had been prowling around the basement where he lived. They were clearly unsettled, growling and with raised hackles. The caretaker wondered if a burglar had been trying to break into the building. The intruder was not human, and although nobody saw anything, the dogs sensed it.
Moral of the story – never mess around with an Ouija board because it opens up the portal to demons. When under demonic attack, turn to God and pray in the powerful name of Christ Jesus.
Summary: Jehovah’s Witnesses (anointed or otherwise) are not immune to demonic possession. However, since the miraculous gifts of the spirit and unusual demonstrations of its power passed away, they believe that “true Christians” do not practice exorcisms. They also denounce any activity by spirit mediums.