Actually, no particular sin is a ticket to hell. It is one's unrighteous position before God---that is, whether or not one has been made righteous by the blood of Jesus Christ through faith in Him. God doesn't judge a person for his sins, but by His "legal" standing before Him. A Christian is only judged for the quality of his works, whether they were done through a motive to bring glory to God or not. That judgment is at its own particular set time. A sinner is judged for his standing, whether righteous or unrighteous. His judgment occurs at the end of all things.
So, a Christian who has suffered great upheaval emotionally, and has fallen to sickness of the mind and commits suicide will be received by the Lord, just as any other Christian who dies due to illness.