No Abraham is not a Christian. We must understand that the following administrations have different time periods in the Bible and each have their own beginning and their own ending—with the exception of the last one.
The first is called the Paradise administration. It was the time of innocence, the time before the fall that ends with Adam and Eve being expelled from the garden of the original paradise.
The second is the Patriarchal administration. It was the time after the fall from the Garden of Eden, but before the Law was given. This second administration ended with the coming of the Law to Moses.
The third is the Legal administration. It's suited only to Israel under the Law, and is sometimes called the Mosaic Law that terminated when Jesus Christ died.
The fourth is the Christ administration that overlapped and functioned within the Law administration. Both the Law and the Christ administration officially ended with the coming of Pentecost.
The fifth started on the day of Pentecost as recorded in the second chapter of the book of Acts. This is the present administration of Grace that is for the Church of God. It's the time period you and I now belong to because it's the Grace administration, without any distinction made between the Jew and the Gentile, which will end with the appearing of Jesus Christ.
The sixth begins with the appearing of Jesus Christ, and the gathering together of the saints. Believe it or not, this administration ends with Satan destroyed, and the great white throne judgment.
The seventh is the Glory or Paradise administration, which will not have an ending.
Administrations must be adapted to the time periods in which they are carried out. The administration with Adam before the fall was different from the one with his immediate family after the fall. The administration with Israel “under the law” was carried out on different principles from the present administration of Grace. This present administration is different from the one that will characterize the return of Christ. The administration of Judgment will be different from the one that will belong to the administration of Glory, when all things shall be gathered together in one under the headship of Christ.
We will never understand the truth of God’s Word if we neglect to rightly divide the subject matter. As far as we are concerned in this Grace administration, what happened to Israel in the Old Testament was written for our learning. If we do not rightly divide to whom it's addressed—the Jew, Gentile, or the Church of God, we will use one truth to contradict another truth, and we will use what is true for one group in contrast to what is also true for another group.
These different administrations are suited to different times because God has spoken everything to its proper time and administration. We will never understand the truth of God’s Word if we read into one administration what God tells us belongs to another administration. If we believe what God said in one administration and carry it into another administration that was on a different principle, we will be taking what is true for one time, and using it to contradict what is also true for another time. When we mix them all together, by jumbling the whole Bible together: Law, Gospel, Grace, Judgment, Glory, Jew, Gentile, and the Church of God, we will be very confused in our understanding of the truth of God’s Word.