Is it possible to be a true believer (saved) without the Holy Spirit being in the believer?
No, Romans 8 makes it clear that no one can possess salvation without being possessed by the Holy Spirit.
9 But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His. 10 And if Christ is in you, the body is dead because of sin, but the Spirit is life because of righteousness. 11 But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you.
Sonship Through the Spirit
12 Therefore, brethren, we are debtors—not to the flesh, to live according to the flesh. 13 For if you live according to the flesh you will die; but if by the Spirit you put to death the deeds of the body, you will live. 14 For as many as are led by the Spirit of God, these are sons of God. 15 For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out, "Abba, Father." 16 The Spirit Himself bears witness with our spirit that we are children of God, 17 and if children, then heirs—heirs of God and joint heirs with Christ, if indeed we suffer with Him, that we may also be glorified together. Romans 8:9-17
The Holy Spirit’s presence in the believer reveals who is saved to God, the angels, and the demons but not to humans. This is called the SEAL of God.
13 In Him you also trusted, after you heard the word of truth, the gospel of your salvation; in whom also, having believed, YOU WERE SEALED WITH THE HOLY SPIRIT OF PROMISE, 14 WHO IS THE GURANTEE OF OUR INHERITANCE until the redemption of the purchased possession, to the praise of His glory. Ephesians 1:13-14
Then how do humans know who is possessed by the Holy Spirit and who is saved? It is evidenced to humans through godliness and loving faith works. What’s that? It’s a life that shows the exterior evidence of the interior dwelling of the Holy Spirit and newly created human spirit.
The true believers will begin to love God more than they love themselves. They will begin to love all their brothers and sisters in Christ. They will begin to love their neighbors as they love themselves. Husbands will love their wives like Christ loves the church. Wives will honor their husbands and teach their children about Christ.
The true believers will grow in grace and knowledge of our Lord and Savior Jesus Christ. As they grow in this knowledge they will seek God’s wisdom, which will be granted then they will begin to draw nearer and closer to our Heavenly Father. As they draw closer to the holiness of the Holy One, they will begin to sin less. They will finally see their utter hopelessness and begin to walk in faith and hope of Christ living His gloriously holy life through them.
This my friend is how you can know someone is born again and are possessed by the Holy Spirit. Every true believer is filled with the Holy Spirit all day, every day. The problem arrives with who is in control of your soul and body which the Bible calls the conscience and flesh.