Perhaps the question should be, Does God answer an unsaved persons prayer?
An unsaved person is one that has never been born again and is not a child of God. Nowhere in all the scripture does it tell one to pray who is not a child of God.
1Pet, 3:12, "For the eyes of the Lord are toward the righteous, And His ears attend to their prayer,
But the face of the Lord is against those who do evil."
The gospel of Christ is Gods' power to save to everyone, Romans 1:16.
Christ told the apostles what to teach in order to save people:
Mark 16:15, And He said to them, "Go into all the world and preach the gospel to all creation.
16 He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned.
Matt. 28:19, Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit,
20 teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age."
Acts 2:37, Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, "Brethren, what shall we do?"
38 Peter said to them, "Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit.
Gal 3:26, For you are all sons of God through faith in Christ Jesus.
27 For all of you who were baptized into Christ have clothed yourselves with Christ
Faith, confession, repentance and baptism puts one into Christ, which is his body the church where they have the forgiveness of sins. Eph. 1:7. Col 1:13, For He rescued us from the domain of darkness, and transferred us to the kingdom of His beloved Son, 14 in whom we have redemption, the forgiveness of sins.
Once a person becomes a child of God He will hear and answer their prayers.
1 John 1:7, but if we walk in the Light as He Himself is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin.
8 If we say that we have no sin, we are deceiving ourselves and the truth is not in us.
9 If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.
10 If we say that we have not sinned, we make Him a liar and His word is not in us.
In the 10th chapter of Acts is the story of Cornelius, how he was a just man and one that prayed to God continually, but he was not saved. God heard his prayer, but did not save him by that prayer but rather sent Peter to him and preached the gospel to him. He believed it, was baptized into Christ and was saved thereby..
Notice though that Cornelius was a devout and just man and God answered his prayer by sending him someone who would tell him words whereby he could be saved.
Acts 10:13, And he reported to us how he had seen the angel standing in his house, and saying, ‘Send to Joppa and have Simon, who is also called Peter, brought here;14 and he will speak words to you by which you will be saved, you and all your household.’