I do believe that God hears the prayers of sinners, because He is God. He hears all things, sees all things and knows all things. When I refer to a sinner I mean someone who is outside the body of Christ and who has never accepted Him as Lord and has never obeyed the will of God. I believe that those who have gotten saved and are in a back slidden state still have the privileges of every believer.
I do not believe that He answers the routine prayers of sinners because the word says:
1. Proverbs 15:29, Psalms 66:18, Proverbs 15:8-9, Psalms 34:15-16,
2. 1 Peter 3:12 -For the eyes of the Lord are over the righteous, and his ears are open unto their prayers: but the face of the Lord is against them that do evil.
I do believe that God draws the sinner and there may be times, when the sinner believes that God has heard them and He was simply drawing them. Jer 31:3 The Lord hath appeared of old unto me, saying, Yea, I have loved thee with an everlasting love: therefore with loving-kindness have I drawn thee. KJV
If He will respond to sinners, then why would they need to get saved? They could just keep living their fun sinful life and just cry out to God in distress.