Yes, these Gentiles in Acts 10:43-47 clearly
believed, received the gift of the Holy Spirit and were saved BEFORE receiving water baptism. Before these Gentiles were water baptized they had already "received" the Holy Spirit (Acts 10:47). In view of this, there are three passages that demonstrate they were already saved BEFORE receiving water baptism.
Romans 8:9 - 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. If one has the Holy Spirit they "belong" to Christ. To belong to Christ does not describe the condition of a lost unbeliever but a saved believer -
such was the case of these Gentiles BEFORE they were water baptized.
Galatians 4:6 - And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out, "Abba, Father!" God sent the Holy Spirit into their hearts whereby they can now rightly refer to God as "Abba! Father!" This does not describe the condition of a lost unbeliever but a saved believer -
such was the case of these Gentiles BEFORE they were water baptized.
1 John 4:13 - By this we know that we abide in Him, and He in us, because He has given us of His Spirit. Because these Gentiles had received the Holy Spirit, they abided in God and God abided in him. To abide in God and to have God abide in you does not describe the condition of a lost unbeliever but a saved believer -
such was the case of these Gentiles BEFORE they were water baptized.
The evidence is overwhelming that these Gentles had believed, received the gift of the Holy Spirit and were saved and a part of the body of Christ BEFORE water baptism. Certain Jews may have wanted to forbid them from being baptized because of their unacceptance of these Gentiles, but Peter clearly states that SURELY NO ONE CAN REFUSE.
These Gentiles were clearly SAVED BEFORE WATER BAPTISM and the Holy Spirit was proof of this.
In addition to receiving the gift of the Holy Spirit, these Gentiles spoke in tongues, which is a spiritual gift that is ONLY for the body of Christ (1 Corinthians 12). *Lost unbelievers DO NOT receive the gift of the Holy Spirit or the spiritual gift of tongues.
In regards to baptism in Jesus name, to act by the authority (in the name of) one is to act by the authority (in the name of) the Father, Son and Holy Spirit, for it is the same authority. There are three separate and distinct individuals in the Godhead (Father, Son, Holy Spirit) all of whom authorize the same act in the same way. So "in Jesus' name" is not a formula for what must be specifically stated when baptizing a person. "In Jesus name" simply means by Jesus' authority or power. So to baptize in accordance with Jesus' name is to baptize according to His power or authority, which is the same as baptizing according to the name or authority or power of the Father, Son and Holy Spirit. - Matthew 28:18-19.
Oneness Pentecostal theology maintains that baptism must be by immersion using the specific formula "in Jesus name" and not "in the name of the Father, the Son, and the Holy Spirit" as Jesus commanded in Matthew 28:19. They reject baptism in the name of the Father, Son and Holy Spirit because they reject the Trinity and the words of Jesus in Matthew 28:19.
I was once approached by a Oneness Pentecostal on my mail route who asked me if I was a Christian and when I said yes, she then asked me if I was baptized in "Jesus name only" and when I said I was baptized in the name of the Father, Son and Holy Spirit, she explained to me that my baptism was invalid and she instructed me to go home and read Acts 2:38 and be sure to get re-baptized in "Jesus name only" and implied that if I don't, then I won't be saved. Now that is getting into legalism!