Does genuine belief in Christ actually play a major role in salvation? Do we actually have to believe in this guy?
Jesus, teaching a crowd of Jews being riled up by the Pharisees, said this to the few who believed and put their faith in Him, 'If you hold to my teaching, you really are my disciples. Then you'll know the truth, and the truth with set you free.' John 8:30-32
Considering Jesus claimed to be the Light of the world in the midst of this discussion and the heated resistance to His testimony - I would say actual, legitimate, personal, rational belief intersects with salvation in a direct way.
The author of Hebrews follows up on this topic by noting that all those under Moses who disobeyed, rebelled and sinned ultimately died in the desert physically and spiritually 'because of their unbelief.' Hebrews 3:16-19.
To those who read, hear or see the message of Christ, Jesus is saying, 'Today...do not harden your hearts.'
Salvation is a vital gift. You and I don't have to accept it, but if we do...we have to believe it's real.