I believe that it does. Lots of Calvinists and Reformed folk believe the same. I do not think that it is a matter of salvation. Most Calvinists, I believe, would hold the same view. Probably why most of us do not spend a lot of time destining those who hold other views to hell.
I will take your word for it. Easy to check, not worth the effort. But, so what? You have as a pet doctrine the "Re-imputation of Sin." That term is found how many times in Scripture? The concept is found how many times in Scripture? To the best of my knowledge, the answer to both questions is zero. Feel to correct me if I am incorrect, but if your argument against Calvinism hinges at all on the number of occurrences of the term, then for the sake of intellectual honesty, it had better be greater than four.
Different term, but same meaning, I believe: Acts 13:48 speaks to the issue...
New International Version
When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed.
New Living Translation
When the Gentiles heard this, they were very glad and thanked the Lord for his message; and all who were chosen for eternal life became believers.
English Standard Version
And when the Gentiles heard this, they began rejoicing and glorifying the word of the Lord, and as many as were appointed to eternal life believed.
Berean Study Bible
When the Gentiles heard this, they rejoiced and glorified the word of the Lord, and all who were appointed for eternal life believed.
Berean Literal Bible
And the Gentiles hearing it were rejoicing and glorifying the word of the Lord, and as many as were appointed to eternal life believed.
New American Standard Bible
When the Gentiles heard this, they began rejoicing and glorifying the word of the Lord; and as many as had been appointed to eternal life believed.
King James Bible
And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
Holman Christian Standard Bible
When the Gentiles heard this, they rejoiced and glorified the message of the Lord, and all who had been appointed to eternal life believed.
International Standard Version
When the gentiles heard this, they began rejoicing and glorifying the word of the Lord. Meanwhile, all who had been destined to eternal life believed,
NET Bible
When the Gentiles heard this, they began to rejoice and praise the word of the Lord, and all who had been appointed for eternal life believed.
Aramaic Bible in Plain English
And as the Gentiles were hearing, they were rejoicing and glorifying God, and they that were appointed to eternal life believed.
GOD'S WORD® Translation
The people who were not Jews were pleased with what they heard and praised the Lord's word. Everyone who had been prepared for everlasting life believed.
New American Standard 1977
And when the Gentiles heard this, they began rejoicing and glorifying the word of the Lord; and as many as had been appointed to eternal life believed.
Jubilee Bible 2000
And when the Gentiles heard this, they were glad and glorified the word of the Lord, and as many as were ordained to eternal life believed.
King James 2000 Bible
And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
American King James Version
And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
American Standard Version
And as the Gentiles heard this, they were glad, and glorified the word of God: and as many as were ordained to eternal life believed.
Douay-Rheims Bible
And the Gentiles hearing it, were glad, and glorified the word of the Lord: and as many as were ordained to life everlasting, believed.
Darby Bible Translation
And [those of] the nations, hearing it, rejoiced, and glorified the word of the Lord, and believed, as many as were ordained to eternal life.
English Revised Version
And as the Gentiles heard this, they were glad, and glorified the word of God: and as many as were ordained to eternal life believed.
Webster's Bible Translation
And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life, believed.
Weymouth New Testament
The Gentiles listened with delight and extolled the Lord's Message; and all who were pre-destined to the Life of the Ages believed.
World English Bible
As the Gentiles heard this, they were glad, and glorified the word of God. As many as were appointed to eternal life believed.
Young's Literal Translation
And the nations hearing were glad, and were glorifying the word of the Lord, and did believe -- as many as were appointed to life age-during;
I believe that the Reformed system has the best overall explanation of the total teaching of Scripture. Yes there are hard parts and verses. But that would be true of any theological system.
At any rate, grabbing a handful of scriptures and making a doctrine out of them is a lot more sound than take a handful of no Scriptures and making a doctrine out of one's vain imagination, see above regarding the Re-imputation of Sin Doctrine.
Calvinists and Reformed folk accept that Jesus Christ is the only means of our salvation.
If that were true then why do you need Calvinism?