Can a person be saved and still be stained with sin? No. If a person has not been washed clean of their sin, then they have not been saved. So, if sin is washed away during baptism then salvation occurs during baptism, not before. There is absolutely no Scriptural support that I have ever seen, or that anyone who supports the idea has ever been able to present, for the "sinners prayer"; it is not a Scriptural concept. There is nothing wrong with getting someone to the point where they will say a prayer like it, but that just puts them at the point of acknowledging their sin and guilt, but now they need to obey the Gospel and be baptized into Christ in order to receive forgiveness (Acts 2:38), and to be united with Jesus' death and resurrection (Rom 6:1-4, Col 2:11-14). That is what constitutes calling on the name of the Lord, obedience to Him in the things that HE says lead to receiving salvation: belief in Jesus (John 3:16 and many others), repentance (Acts 3:19), confession of Jesus as Lord (Rom 10:9-10), and baptism (in water)(Acts 2:38, 1 Pet 3:21, Mark 16:16, and others).