First of all, what elirat49 describes in the OP is not atheism but rather agnosticism... The difference being that atheists (a- = not; theist = belief in a god) don't believe in a god whatsoever whereas agnosticism (ag- = not; nost = knowledge) believes that we as humans cannot know god fully although they might believe in the existence of a god or other higher power.
As for your question, the answer will also depend on the answerer's own religious beliefs. Some belief systems condemn anyone that doesn't have the exact same belief structure as themselves; even if both were Christians, some Christian doctrines would condemn their fellow Christian as being a heretic and therefore bound for hell.
As a Catholic, I believe that atheism and agnosticism are sins, but that doesn't necessarily mean that they are mortal sins (sins so horrible that it keeps a person's soul out of heaven). As countrygirl12 said "... every one sins. No one is perfect." Just because a person sins doesn't mean that they are therefore bound to hell. When Jesus said that the only way to God is through him, Catholics believe this more in the abstract sense than a concrete expression of belief: to go to God / heaven through Jesus means more that a person lives their life according to Jesus' teachings rather than actually believing in Jesus' divinity. So a person living in the rural farmlands of China that may have never read the Bible nor heard any of its teachings may still be able to go to heaven if they still live their lives by loving their fellow man, forgiving those that hurt them, etc. (ie by living a life exemplified by Jesus even if the person knows not of what that means). Similarly atheists / agnostics that don't believe in God may still be able to enter into heaven if they too live a "Christian" lifestyle.
Oftentimes (esp. nowadays, after the Enlightenment Period) people are atheists or agnostics because they only believe in what they can see or what can be described by science. They want to reserve their judgement until that proof is produced, either when they die and are standing before the gates of heaven, or at the end of time. These people can enter heaven since their sin isn't so terrible; after all, even one of Jesus' apostles is known as "Doubting" Thomas because he didn't believe in Jesus' resurrection until he could examine the nail-holes in Jesus' hands from His crucifixion.
Where being an atheist / agnostic may be bound for hell is if they truly reject God and His teachings. If a person believed completely in the "survival of the fittest" even to the point as accepting murder, theft, etc. as justified in that the perpetrator must have some strength over the victim and therefore is the fittest person and thus should survive and thrive, they are then fully rejecting God and therefore cannot enter into heaven.