The simple answer is "yes", but it's important to examine the issue more closely.

Jesus provided salvation for the entire world of mankind by paying the ransom price for us. "For as in Adam, all die, even so in Christ, shall all be made alive,.: 1 Corinthians 15:22. "For there is one God and one Mediator between God and men, the man Christ Jesus, who gave Himself a ransom for all to be testified in due time:"1 Timothy 2:5. Thus we can see that first, the ransom from death applies to every human being, but the "due time" for it to be testified, or revealed has not yet come. Peter tell us (2 Peter 3:13) that we "look for a new heavens and a new earth in which righteousness dwells." During that Kingdom, which lasts a thousand years, all the resurrected of the earth and "will know the Lord from the least to the greatest" Hebrews 8:11

Yet, we are all familiar with John 3:16, "For God so loved the world that He gave His only begotten son, that whoever believes in Him will have everlasting life." Thus we see that accepting the ransom given is a qualification for the joys offered. The Scriptures abundantly show that ample time and opportunity for understanding and overcoming their individual pasts will be given. Yet after sufficient nurturing and education has been given, "…evildoers shall be cut off, but those who wait on the Lord, they shall inherit the earth." Psalm 37:9.

But what about Christians now, who are striving to follow in Jesus's footsteps to be joint-heirs with Him in the heavenly Kingdom? Paul acknowledged that even he was vulnerable if not faithful. In 1 Corinthians 9:27 he says, "…I discipline my body and bring it into subjection, lest when I have preached to others, I myself should become a castaway."  If even Paul could be judged unfaithful, we, too, could lose our salvation if we don't cherish our relationship with the Lord, if we reject His ransom for us, if we turn away from the holy things and wallow again in the evils of the earth. 

God's overall principle is summarized in Romans 6:23, "For the wages of sin is death, but the gift of God is eternal life through Jesus Christ our Lord."  See also Deuteronomy 30:15, 16, 19, and 20.