Summary: No. If a person is spirit-begotten and then allows demons to rule him, he will die the second death. But God, out of love, will send many severe trials to bring that one to repentance before that happens. However, a person may still chose to follow evil, forsake God, and become demon-possessed.
Discussion: Many people recognize Jesus as their Savior, strive to live righteously, and believe they are true Christians. This is an excellent first step, but it is insufficient to become spirit-begotten. Romans 12:1-2 teach a next step. Romans 12:1-2 NKJV), “I beseech you therefore, brethren (brethren are already believers in Christ), by the mercies of God, that you present your bodies a living sacrifice (sacrifice your will and obey God’s will), holy, acceptable to God, which is your reasonable service.”
Jesus instructed self-denial and cross-bearing. “Then Jesus said to His disciples, ‘If anyone desires to come after Me, let him deny himself, and take up his cross, and follow Me.’” Matthew 16:24 (NKJV) This is much more than righteous living.
When God accepts a person’s vow to lay down his life in sacrifice, then his old man is counted as dead. Then God begets him to a new life with the holy Spirit. Romans 6:6 (NKJV), “knowing this, that our old man was crucified with Him, that the body of sin might be done away with, that we should no longer be slaves of sin.” 2 Corinthians 5:17 (KJV), “Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.”
But if an evil spirit possesses a person, that person no longer is a new creature. Romans 6:14, “…sin shall not have dominion over you…” That poor person has allowed demons to enter him and will go into second death. Hebrews 6:4, 6 (NKJV), “For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, … 6 if they fall away, to renew them again to repentance…”
However, God does not just let His precious Christian children slip away. When His child begins to fall into sin, God corrects him. Hebrews 12:6-7 (CSB), “the Lord disciplines the one he loves and punishes every son he receives. . . God is dealing with you as sons. For what son is there that a father does not discipline?” God mercifully gives that one trials to bring them to their senses. They usually change and repent and see their need to obey God.
So, just because a person calls himself a Christian, does not make him a spirit-begotten new creature. If someone is demon-possessed, he is not necessarily lost. There will be no demons for those receiving the resurrection in the earthly kingdom. All will be taught righteousness. (Jeremiah 31:31-33)