No. Think of all the Old Testament believers who were not baptized—as Baptism had not yet been instituted. Jesus stated that it is the lack of faith, not Baptism, that condemns (Mark 16:16).
We speak of Baptism being necessary in the sense that the Lord commands us to administer it. However, Baptism not absolutely necessary for salvation because the Holy Spirit can bring people to saving faith in Jesus through the gospel in Word alone. In situations like that, people will still want to be baptized—to do what Jesus says and to receive, in addition to the message of the Bible, another guarantee of God’s love and forgiveness in Christ.