My answer would be No. Consider these Bible verses:
John 14:6:
Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.
John 3:18:
"Whoever believes in him is not condemned, but whoever does not
believe stands condemned already because they have not believed in the
name of God’s one and only Son."
1 John 5:12:
Whoever has the Son has life; whoever does not have the Son of God does not have life.
In general Romans 3 gives a more details explanation.
In Vers 10 it says:
as it is written: “None is righteous, no, not one;
And Vers 21 says:
For by works of the law no human being[3] will be justified in his sight, since through the law comes knowledge of sin.
Summarized in vers 21-24:
21 But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—
22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction:
23 for all have sinned and fall short of the glory of God,
24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus,
Also let's pick apart "leads a moral life with equivalent morals to that of a christian" a bit.
Can you imagine a person who does not believe in God but fulfills the most important commandment in the Bible in Matthew 22:36-39:
36 “Teacher, which is the great commandment in the Law?”
37 And he said to him, “You shall love the Lord your God with all your heart and with all your soul and with all your mind.
38 This is the great and first commandment.
39 And a second is like it: You shall love your neighbor as yourself.
So part of Christian morality is to love God. I would presume here that you can't love what you do not believe in.
There is also Romans 2,14-16: (In general read Romans)
14 For when Gentiles, who do not have the law, by nature do what the law requires, they are a law to themselves, even though they do not have the law.
15 They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them
16 on that day when, according to my gospel, God judges the secrets of men by Christ Jesus.
So I would make the case that God is able to consider the situation and context of each person, meaning that if a Person doesn't know anything about God and his law, that person still might have a chance. But the issue is that God still judges that person, instead of Jesus paying the debt for that person. But still, I think God will still be fair about it.
But to sum it up: In general, if you know about God and his law (and that is what you imply by saying "and the Christian faith turns out to be the truth")
and still don't follow God, then you will be judged by God.
If you repent and follow God, God's judgment is fulfilled by the sacrifice of Jesus. To give an analogy: A Person X owes 1 Trillion Dollars and if X does not pay, he will be thrown in jail. Unless X has a friend that pays the money for him, X will be thrown into jail. Now if X has made that rich friend (which is Jesus) then the debt is paid, and X is a free man.
This means the relationship between X and God changes from "defendant before a judge" to "friend of someone who loved X enough to pay 1 Trillion Dollars for".
So while the bible might sound quite harsh at first glance, it provides an easy way out by repenting and following Jesus, while still dealing with sin appropriately. The easiest way to do this practically would be to pray, but I would strongly recommend going to a local church for more guidance.