“The only prayers that God answers are those from His children. The unbeliever has no access to Him because they are not His family. Once a person trusts Christ as Savior, access is available to God and prayers are answered.” - Don Stewart (Blue Letter Bible)
John MacArthur says generally, no.
“...[D]oes God answer the prayers of unbelievers? A strict yes or no answer is difficult without qualifying the answer in various ways. ... [We] can safely say that, in general, God does not answer the prayers of an unbeliever.” - John MacArthur (Grace To You)
Does God hear the prayers of unbelievers?
“…if Jesus is the only mediator between God and man, will God hear the prayers of those who do not trust in Jesus? The answer depends on what we mean by ‘hear.’ Since God is omniscient, he always ‘hears’ in the sense that he is aware of the prayers made by unbelievers who do not come to him through Christ. God may even, from time to time, answer their prayers out of his mercy and in a desire to bring them to salvation through Christ. However, God has nowhere promised to respond to the prayers of unbelievers. The only prayers that he has promised to ‘hear’ in the sense of listening with a sympathetic ear and undertaking to answer when they are made according to his will, are the prayers of Christians offered through the one mediator, Jesus Christ (cf. John 14:6).” (Systematic Theology by Wayne Grudem, 1994. pg. 378)