It is not possible to “repent and be baptized” (Acts 2:38) unless we first believe. “How then will they call on him in whom they have not believed?” (Romans 10:14) So conviction is essential before conversion.
However is it possible to be convinced and yet refuse to convert? Judas Iscariot is a notable example. He took his own life when he realised what a wicked thing he had done. He showed conviction, but not conversion. If Judas had shown the same love for Jesus and all that Jesus stood for, as was exhibited by his fellow disciple Peter, then he would have repented and been forgiven. There is such a thing as an unforgiveable sin, but only a sin that we refuse to repent of because we choose not to love Jesus. The principle of the unforgivable sin is outlined in Jesus’s answer in Matthew 12 to the attribution by the Pharisees of Jesus’s miracles as being from an evil force. They acknowledged the power; a sort of conviction. And yet they refused to be converted because they hated Jesus. This was blasphemy against the Holy Spirit, and will not be forgiven.
However even though we are convinced and we love Jesus and be converted we can still slide back into evil behavior. As long as we want to come back to God repentance remains possible no matter how serious is our crime.