So are you saying that a believer that has accepted Jesus as his Lord and Savior is not saved if he has not been baptized??
That's up to God.
Jesus promises that if we believe and baptised we will be saved.
There are many possibilities why someone may believe and not be baptised. Whether God saves them is up to God but wilfull refusal to be baptised is disobedience which is disbelief.
Jesus gives us a pattern for our salvation
“Go into all the world and preach the gospel to every creature. He who believes and is baptized will be saved; but he who does not believe will be condemned.”
In these words Jesus sets out the basic methodology our initial justification (salvation)
preach the gospel;
believe the gospel; be
baptised.
We can see these three steps in the Acts of the Apostles, either explicitly or implicitly.
At Pentecost (Acts 2:14-40)
Philip in Samaria (Acts 8:5-12)
Philip with the Ethiopian (Acts 8:26-38)
Cornelius (Acts 10:34-48)
Lydia (Acts 16:13-15)
The Jailer (Acts 16:30-33)
12 men at Ephesus (Acts 19:1-5)
The first step is to hear the gospel which is why Jesus places preaching it first. We can infer from those words that what Jesus says next only applies to those who have had the (true) gospel preached to them and are capable of understanding it.
Then there are four possibilities:
1. Someone believes and is baptised.
2. Someone believes but is not baptised.
3. Someone does not believe and is baptised.
4. Someone does not believe and is not baptised.
Jesus only definitively addresses 1. & 4, although some may argue that 3 is included in the
not believe statement. However that requires a deeper understanding of the sacrament of baptism. But regarding this thread Jesus definitively states that for those to whom this applies (hearing and understanding the true gospel) then both faith and baptism are the normal way to receive salvation.