Isn't God's Word pretty clear about the work of the Holy Spirit wooing mankind to believe on Christ?
International Standard Version (©2008) John 6:44
No one can come to me unless the Father who sent me
draws him, and I will raise him to life on the last day
King James Version.. 1 Corinthians 2:10
But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God.
Wherefore I say unto you, All manner of sin and blasphemy shall be forgiven unto men: but the blasphemy against the Holy Ghost shall not be forgiven unto men. And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come" [SIZE=-1](Matthew 12:31-32).[/SIZE]
When one rejects Christ, it is the Holy Spirit's wooing that is being rejected. It is that sin that is unpardonable, being that of failing to accept Christ's redeeming work on the cross and resurrection.
If only believer's can hear God, no one could be saved. The Holy Spirit IS God, remember, and is the very Person who draws us to the Love that provides the grace and mercy to forgive us. Can a person who has not obtained eternal life understand God's Word? Not really.
For the natural man receives not the things of the Spirit of God, for they are foolishness unto him , neither can he know them for they are Spiritually discerned. 1 Corinthians 2:14 For this very reason we are not to debate nor argue etc with someone who is not a believer, but preach Christ crucified, risen and coming again. That is the only message they can truly hear until they find Christ.
Another thought on this is that I would encourage those wondering about this to study how people do not have to be a believer (read saved, born again, follower of Christ etc) to be a recipient of God's miracles. All around us and specifically, God gives miracles to unbelievers to bring them to Himself. Through the miracle, and the Holy Spirit, the unbeliever comes to Christ.
SO if God can do all this, what does He need us for? It is His preferred method ...for those to hear of His greatness through believers. If He didn't need us, as lights (not hid under bushels) as soon as someone accepted eternal life, they would be taken out of the world immediately, since there would be no "reason" for them to have to suffer further. We are His workmanship, created to do the work of Christ here on earth. (Ephesians 2:10)
However the main purpose of any Christian is to worship God and to bring others to finding Him as well. Not all are called as evangelists, but all are called to evangelize. ;) A pastor, in the technical sense, is not an evangelist. Billy Graham spoke to the definition of the difference, and I agree with him in that an evangelist must stick to the Gospel of Christ, the Cross, Christ's death, burial and resurrection to win others. A pastor and each believer has their own path that includes winning others, but not necessarily as their only and main goal in life.
I trust all Scriptures are within context.