Yes, but only if we are Christians before the suicide. Yes, but only if we were Christians. These are valid questions, especially in this age when suicide is on the rise. First, we must bear in mind that suicide is simply self-inflicted murder, usually premeditated. Believers can commit murder.
Christians can commit any sin of which the heart is capable.
A person is saved by the grace of God when they repent, believe and submit to the Lordship of Christ. Before the earth was even formed God determined who would be redeemed and who would be left in their lost condition. Man cannot change God's sovereign choice. One's eternal life depends on God's grace and Christ's redemptive work, not a person's last act before death. Suicide is not an unpardonable sin.