Does Matt 7:23 teach that God doesn't in fact intimately know everyone?

God knows everything about everyone. What He is referring to is that a person professing to be born again should have His Holy Spirit. "Workers" of iniquity do not have the Spirit of God. Romans 8:29 is talking about the person who really is saved, who really does have the Holy Spirit. That person learns to live like and to be a reflection of the life of Jesus.