No, because there are numerous examples in Acts, the Gospels, and other New Testament books where people asked what must I do to be saved say that it is belief and repentance is necessary for salvation.
Acts 16:29-31 The jailer called for lights, rushed in and fell trembling before Paul and Silas. He then brought them out and asked, “Sirs, what must I do to be saved?â€
They replied, “Believe in the Lord Jesus, and you will be saved —you and your household.â€
This is a good text to bring up! Let's look at the fuller context:
And he called for lights and rushed in, and trembling with fear he fell down before Paul and Silas, 30 and after he brought them out, he said, “Sirs, what must I do to be saved?†31 They said, “ Believe in the Lord Jesus, and you will be saved, you and your household.†32 And they spoke the word of the Lord to him together with all who were in his house. 33 And he took them that very hour of the night and washed their wounds, and immediately he was baptized, he and all his household. 34 And he brought them into his house and set food before them, and rejoiced greatly, having believed in God with his whole household. Acts 16:29-34
So there's this earthquake and all the prisoners chains had been released and this poor jailer is going to kill himself rather than face the consequences of having all his prisoners escape on his watch.. when Paul assures him that they are all there.
He asks, "What must I do to be saved?" and Paul answered, "Believe in the Lord Jesus and you will be saved, you and all your household."
Then... (because that's not the end of the story)... Then Paul further shared the gospel, "spoke the word of the Lord", not just to the jailer but to all who were in his house (I've always imagined that the jailer lived right there in the jail).
After speaking the word of the Lord to them, their response... and this is important, their response was to be baptized. All of them, the whole household. Luke uses the word "immediately". No waiting around, no taking classes... The jailer and his household had the full gospel shared to them, they believed and their first response was to be baptized.. right then and there.
This is not unlike the episode with the Ethiopian official:
But an angel of the Lord spoke to Philip saying, “Get up and go south to the road that descends from Jerusalem to Gaza.†(This is a desert road.) 27 So he got up and went; and there was an Ethiopian eunuch, a court official of Candace, queen of the Ethiopians, who was in charge of all her treasure; and he had come to Jerusalem to worship, 28 and he was returning and sitting in his chariot, and was reading the prophet Isaiah. 29 Then the Spirit said to Philip, “Go up and join this chariot.†30 Philip ran up and heard him reading Isaiah the prophet, and said, “Do you understand what you are reading?†31 And he said, “Well, how could I, unless someone guides me?†And he invited Philip to come up and sit with him. 32 Now the passage of Scripture which he was reading was this:
“ He was led as a sheep to slaughter;
And as a lamb before its shearer is silent,
So He does not open His mouth.
33 “ In humiliation His judgment was taken away;
Who will relate His generation?
For His life is removed from the earth.â€
34 The eunuch answered Philip and said, “Please tell me, of whom does the prophet say this? Of himself or of someone else?†35 Then Philip opened his mouth, and beginning from this Scripture he preached Jesus to him. 36 As they went along the road they came to some water; and the eunuch *said, “Look! Water! What prevents me from being baptized?†37 [And Philip said, “If you believe with all your heart, you may.†And he answered and said, “I believe that Jesus Christ is the Son of God.â€] 38 And he ordered the chariot to stop; and they both went down into the water, Philip as well as the eunuch, and he baptized him. 39 When they came up out of the water, the Spirit of the Lord snatched Philip away; and the eunuch no longer saw him, but went on his way rejoicing. Acts 8:26-39
"What prevents me from being baptized?"
Well, nothing, nothing at all.... there was a supply of water, so Philip took him down into the water and baptized him.
What prevents anyone from being baptized? Probably because the Church has muddied the baptismal waters with way too much theology and not enough just getting it done.
The question, "Do you have to be baptized to achieve salvation?" must technically have the answer "no" because we all know the thief on the cross was saved and yet wasn't baptized.
I've said this before... unless you're planning on spending your entire walk with Christ on this earth dying on a cross, you need to be baptized.
Refusing to be baptized is a problem. As Tina says, if a believer is refusing to be baptized, his salvation is questionable.