Can someone like Cornelius be righteous through general revelation, without knowledge of Christ?

Yes. Paul already told us in Romans 1 and Romans 2 that God wrote his laws on the heart of men, and that includes both worship laws and moral laws; the first three commandments and the last seven are written on the heart of man from the day he is conceived, on his soul. Adam had it when he was created, because he had to have some way to know how to obey God when God told him not to eat the fruit; his conscience told him, and the law was written on his heart both to worship God and to obey what God says. That is how he knows, long before Jesus Christ comes on the scene as a man. So yes, Cornelius can act righteously before God, just as Noah did in Genesis 6, where God looked out and saw the most righteous man on earth, which is why God saves him and his family, long before Jesus came. Job is the same way: God says to the devil, have you seen my servant Job, the most righteous man in the east, and gives the devil a blank check over him except to take his life. So God was calling them righteous long before Jesus came.