No, unsaved people cannot commit truly "self-less" acts. (But neither can saved people really).

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Benjamin P. Glaser
Pittsburgh, PA,
Fairmount ARP Church
Candidate Under Care Pittsburgh Theological Seminary & Reformed Presbyterian Theological Seminary
"The benefit of deliverance becomes the more precious in the same proportion in which we are brought to apprehend the magnitude of the evil from which we have been rescued"
-- Zacharias Ursinus, Commentary on the Heidelberg Catechism