Absolutely.
As Greek scholar AT Robertson stated: This phrase is the subject of endless controversy as men look at it from the standpoint of sacramental or of evangelical theology... Change of number from plural to singular and of person from second to third. This change marks a break in the thought here that the English translation does not preserve.
The first thing to do is make a radical and complete change of heart and life. Then let each one be baptized after this change has taken place, and the act of baptism be performed “in the name of Jesus Christ” (εν τωι ονοματι Ιησου Χριστου — en tōi onomati Iēsou Christou).
So I understand Peter to be urging baptism on each of them who had already turned (repented) and for it to be done in the name of Jesus Christ on the basis of the forgiveness of sins which they had already received.
Acts 2:38 (KJV) - Robertson's Word Pictures (NT)
On the surface it may sound like it but after a closer look we see otherwise. In Acts 2:38, "for the remission of sins" does not refer back to both clauses, "you all repent" and "each one of you be baptized," but refers only to the first. Peter is saying "repent unto the remission of your sins," the same as in Acts 3:19. The clause "each one of you be baptized" is parenthetical. This is exactly what Acts 3:19 teaches except that Peter omits the parenthesis.
*Also compare the fact that these Gentiles in Acts 10:45 received
the gift of the Holy Spirit (compare with Acts 2:38 -
the gift of the Holy Spirit) and this was BEFORE water baptism. (Acts 10:47)
In Acts 10:43 we read
..whoever believes in Him receives remission of sins. Again, these Gentiles received
the gift of the Holy Spirit - Acts 10:45 -
when they believed on the Lord Jesus Christ - Acts 11:17 - (compare with Acts 16:31 -
Believe on the Lord Jesus Christ and you will be saved) BEFORE water baptism - Acts 10:47. This is referred to as
repentance unto life - Acts 11:18.
*So, the only logical conclusion
when properly harmonizing scripture with scripture is that faith in Jesus Christ "implied in genuine repentance" (rather than water baptism) brings the remission of sins and the gift of the Holy Spirit (Luke 24:47; Acts 2:38; 3:19; 5:31; 10:43-47; 11:17,18; 13:38,39; 15:7-9; 16:31; 26:18).
*Perfect Harmony*
These Gentiles in Acts 10 had already believed, received the gift of the Holy Spirit, spoke in tongues (spiritual gift that is ONLY for the body of Christ - 1 Corinthians 12) and were saved BEFORE water baptism. The truth here is crystal clear.
These Gentiles speaking in tongues was a confirmation to the Jewish believers that God had accepted these Gentiles into the body of Christ.
There certainly is remission of sins in Acts 10:43 - Of Him all the prophets bear witness that through His name everyone who
believes in Him receives remission of sins.