What is the role of [your] kind of apologetics in convincing someone to become a Christian?
Apologetics is a very powerful tool, but it's ultimately janitorial. Many people encounter obstacles to the faith. Think of the Christian, for example, who loses a relative and is assailed by the question, Why did God allow that? Even the believer can be haunted by difficulties that get in the way of building a relationship with God.
Apologetics can come in and help to make important distinctions and clarify some of the difficulties. You are doing no more than clearing away debris that blocks the door to faith, and ultimately it is God's love that has to work its way into a heart. Conversion ultimately comes from that; apologetics only clears the driveway.
This is a good reminder that while apologetics can be helpful to faith, they are never the object or ground of faith. That belongs only to Jesus Christ.
C.S. Lewis warns about the danger of our faith becoming overly dependent on apologetic arguments, rather than on Christ himself:I have found that nothing is more dangerous to one’s own faith than the work of an apologist…. That is why we apologists take our lives in our hands and can be saved only by falling back continually from the web of our own arguments, as from our intellectual counters, into the Reality – from Christian apologetics into Christ Himself. ("Christian Apologetics" in God in the Dock, p. 103)