No, it is positively not true.
Before we talk about water and Holy Spirit baptism, it's vital to re-establish how a person is saved. The Bible makes it abundantly clear that salvation is obtained by placing our faith in the finished work of Jesus Christ on the cross for the forgiveness of our sins. (See John 1:12-13; Romans 10:9; Ephesians 2:8-9) Jesus paid IN FULL the penalty of our sin, and by placing our faith in his death on our behalf we are saved from bearing our own penalty. When Jesus uttered the words "It is finished" from the cross, He was declaring that the penalty of our sin was paid in full. When we accept by faith that He accomplished all this for us, the Bible declares that our sins are blotted out and we are made children of God.
Water baptism and Spirit baptism come into view after salvation — they do not secure it. In other words, we baptize people who are already saved. It's the same with Spirit baptism. This work referred to as the Baptism of the Holy Spirit is designed to empower believers for service, not to save them.
Here is a link to a teaching (mp3) I did that may help to clear some of the confusion.