Yes.
Acts 2:38 And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. 39 For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.”
It might seem strange to say “yes” without qualification, but that is what Peter says, and there seems no scriptural justification for distinguishing the baptisms of those 3,000 people from baptisms today:
Acts 2:40 And with many other words he bore witness and continued to exhort them, saying, “Save yourselves from this crooked generation.” 41 So those who received his word were baptized, and there were added that day about three thousand souls.
It does not say that those 3,000 “received the gift of the Holy Spirit” (either the Holy Spirit itself being a gift or what the Holy Spirit gives), around the time of their baptism, but we know that being “born of water” and being “born of spirit” are closely and intimately connected:
Titus 3:5 he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit,
John 3:5 Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God.
The exception to this is the disciples themselves who were baptised by John (John 1:37; Acts 1:22) yet did not receive the Holy Spirit until the morning of Christ’s resurrection (John 20:22) four or more years later. This, the gospel writer John notes, was because the Holy Spirit “was not” (or possibly “was not be received”) prior to the resurrection of Christ (John 7:39). This is confirmed by Mark 1:8 “I have baptized you with water, but he will baptize you with the Holy Spirit.”
Whether four years later, like the apostles, or around the time of baptism, or as a process in which baptism is part of the public “good confession” (1 Timothy 6:13), to be given the Holy Spirit is an essential part of new life, new birth in Christ:
Romans 5:5 and hope does not put us to shame, because God’s love has been poured into our hearts through the Holy Spirit who has been given to us.
Ephesians 3:16 that according to the riches of his glory he may grant you to be strengthened with power through his Spirit in your inner being,
“like they did in Acts”
That hopefully answers main part of the question, but there may be a second question arising from the phrase “like they did in Acts”.
The majority of baptisms in Acts are like those 3,000 at Pentecost. They started a new life, were born of water and spirit, but their baptisms were not accompanied by any of the “signs” and “powers” of the Spirit which a few New Testament believers later demonstrated. Even the apostles at Pentecost are a case in point. They received the Holy Spirit on resurrection Sunday (John 20:22) but were told by Jesus to wait in Jerusalem tilll they would be “clothed with power from on high” (Luke 24:49; Acts 1:8)
No one received all three — baptism and the Holy Spirit and powers — at Pentecost; The apostles were already baptised and had the Holy Spirit but not powers. The 3,000 were baptised and received the gift of the Holy Spirit, but not signs or powers of the Holy Spirit. The 3,000 did not speak in tongues. Power was given (as Jesus had said it would be in Luke 24:49 and Acts 1:8) to the those who already had been baptised four years earlier and received the Holy Spirit 47 days earlier (John 20:22).
The exceptions are two other cases in Acts:
- The first Gentile baptisms — these spoke in tongues first and then were baptised:
Acts 10:47 “Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?”
- The first rebaptisms — these 12 men in Ephesus received baptism then Paul laid his hands on them; after which they spoke in tongues and prophesied.
Acts 19:6 And when Paul had laid his hands on them, the Holy Spirit came on them, and they began speaking in tongues and prophesying.
These two cases bear some resemblance (in particular the tongues) to the case of the apostles who, having already “received the Holy Spirit” were 47 days later “clothed with power from on high” (Luke 24:49) “baptized with the Holy Spirit not many days from now.” (Acts 1:5) and “filled with the Holy Spirt” (Acts 1:2).
But then again, the majority of those in Acts did not experience this when they were baptised. In fact neither did the 12 disciples of John in Ephesus; they experienced it when Paul laid his hands on them. And neither did Cornelius; he had already experienced it which led to his baptism with water.
So the answer is perhaps more “like most people in Acts”, since Acts 10:47; 19:6 are two significant events — the first breaking of the covenant of circumcision since Abraham, and the first rebaptism — showing that baptism without having even heard that the Holy Spirit exists was not sufficient.
For the rest of us, the experience of the 3,000 is perhaps more typical:
Acts 2:38 And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.
Other verses show that believers are to “receive the Spirit” and “be in the Spirit” and that the “Spirit dwells in you” (plural)
Romans 8:9 You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him. 10 But if Christ is in you, although the body is dead because of sin, the Spirit is life because of righteousness. 11 If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you.
Romans 8:15 For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!”
1 Corinthians 2:12 Now we have received not the spirit of the world, but the Spirit who is from God, that we might understand the things freely given us by God.
But also Christians must stick with this Spirit, and not accept that which accompanies an alternative Jesus.
2 Corinthians 11:4 For if someone comes and proclaims another Jesus than the one we proclaimed, or if you receive a different spirit from the one you received, or if you accept a different gospel from the one you accepted, you put up with it readily enough.
Galatians 3:2 Let me ask you only this: Did you receive the Spirit by works of the law or by hearing with faith?
And finally that Spirit is also a promise, or deposit, of life to come:
Galatians 3:14 so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promise of the Spirit through faith.