I think this psalm could be used (misused, actually, in my opinion) to slam atheists and make the case that those who have arrived intellectually at the conclusion that there is no God are incapable of good deeds. However, it seems to me that such an approach is not only untrue but much too simplistic. What the psalmist probably has in mind here is something else entirely.
A couple of Scriptural connections can be made. The RCL pairs Psalm 14 this week with the story of David and Bathsheba. That is instructive, because King David was by no modern definition an atheist. Yet his behavior here is certainly foolish--tragically so--and perhaps demonstrates the true intent of the psalmist.
Another connection is with Jesus' parable of the rich fool (Luke 12:16-21). This fellow, having been blessed with abundant harvests, decides to build gigantic barns to store his crops, and to devote himself to his own pleasure. "I... I... my..." reads the man's soliloquy. And God calls him, "You fool!"
The problem the psalmist sees is not intellectual--someone ruling out God's existence through reason and logic--it's behavioral and theological. Wicked actions, including mistreatment of the poor, indicate, in the psalmist's view, what a person believes about God: not so much whether or not God exists, but whether or not God matters. This practical atheism is a problem not just outside communities of faith, but within them.
The challenging question for us is, "How do our actions demonstrate our theology?"