This is not necessarily true. I have met people who were, by their own admission, enjoying their life of sin and having no regrets. By no concerted effort did their heart bring repentance. God stirred them and made them alive (Ephesians 2:4).The person at the point of surrendering is not righteous, God is still his enemy.
You are right to realize the nonbeliever does not really want to surrender, but like the prodigal son his actions have brought him to the pigsty of life and brought him to his senses so he can see where he is headed and does not want to go there so selfishly choses to surrender.
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