Thank you for your Question.
The simple answer is YES!
If He didn’t no one would be heard for we all sin.
Ecclesiastes 7:20 For there is not a just man upon earth, that doeth good, and sinneth not.
Romans 3:23 For all have sinned, and come short of the glory of God;
Romans 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
Jesus died to save us from our sins.
Matthew 1:21 And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.
Matthew 26:28 For this is my blood of the new testament, which is shed for many for the remission of sins.
1Timothy 1:15 This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief.
But he requires a response from sinners.
Mark 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Ac 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins,
1Corinthians 15:1 Moreover, brethren, I declare unto you thegospel which I preached unto you, which also ye have received, and wherein ye stand;
2 By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
Sinners who receive the gospel, repent of their sins and are baptised are required to then walk in the light of that gospel by keeping Christ’s commandments. They will not be 100% successful but continued forgiveness is available.
1John 1:7 But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
8 If we say that we have no sin, wedeceive ourselves, and the truth is not in us.
9 If we confess our sins, he is faithful and just to forgive us our sins, and tocleanse us from all unrighteousness.
If however a sinner deliberately carries on sinning, Christ’s sacrifice will not save him from the consequences of his sin and he will be excluded from the Kingdom of God.
Hebrews 10:26 If we deliberately keep on sinning after we have received the knowledge of the truth,no sacrifice for sins is left, (NIV)
1Corinthians 6:9 Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind,
10 Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God.
Galatians 5:19 Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness,
20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,
21 Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God.
I hope this helps.