probably, because no matter how much "faith" you have, there is always the question "is there really a god?"... billions of years of evolution has gave us all a will to live, otherwise there would be no life without that will.

this is really off of the mark ( with all due respect) the truth is when you become a Christian your life no longer belongs to you. ( he who lays down his life for me............) you dont have the right to choose to die, you have to be content with what God chooses for your life. You live for him and you die for him not yourself. This goes back to fighting your own flesh, even in death you cant place your desires before Gods

You have to understand the makeup of a real Christian in order to answer your question. Sin is in the flesh and the spirit that is saved is from God and now sin free. Both live together until death at which time the sin dies in the flesh and the Christian is freed. Until that time they will have an internal war and are directed to ( fight the good fight of faith) basically sometimes you are in the faith and winning and sometimes you are in the flesh and losing so the answer to your question is YES and they will be. They know they are no good (real ones do) they are just forgiven because of faith.

No one should shove the bible on anyone, God gave each person the right to believe or not. Christians are supposed to live in a way as to show you the love of Christ in their actions, sometimes they will and other times they will lose their personal fight. Many claim it but only God can judge who has faith and who does not. He said you will know them by their fruit.....not daily actions but the product they produce in the long term.