I’m of the unorthodox view that a person who’s never heard the gospel might be granted grace at judgment based on his heart (longing to know the God he hadn’t been formally introduced to); however, if a person has consciously rejected God out of human pride, I really don’t see any number of “good” works offsetting that.
The folks that I talk to about this in 12 step programs usually have rejected all religion because of the concept of a punishing, angry and vengeful God who sacrificed His own son for the sin of Adam was shoved down their throats as children. That, and the John Pipers of the world saying the OK tornado was God's wrath. My sister-in-law says hurricane Sandy is the end times. It goes on.
The reality is the Lord is life itself and love itself. By step 2, we use 'power greater then ourselves'... step 3 is a 'God of our understanding'... by step 4, we find that the punishments on ourselves we blamed God for were our own fault. Just read the book of James - the whole concept sprung from there.
I believe that 'knowing Christ' is understanding and accepting a loving God. We repent and make amends. It's a continuous process. I see God working in those rooms every day.
Pride and arrogance? Sure it exists but it can be turned away from. For the willing.