Brutus,
A yes or no answer is inadequate, so...
I don't know, but strongly believe that the book of life is what I would term a "living document" that is, it is not a bound and sealed book, but one that is added to, whether by simply a check mark next to an existing name, or by the addition of a name.
We are told that names can be blotted from the Book of life, examples below, so the book must be open and living.
If the book is open and living, and names can be blotted out, that must mean that everyone's names are in the book to start with and when we sin against God (perhaps a direct act against God and his chosen race), the names of the actors get blotted from the book. If that is the case, then why can't names be added upon their belief in the Lamb?
[Isa 48:19] Your descendants would have been numbered like the sand, your offspring as many as its grains. Their name would never be cancelled or blotted out from my presence.
[Rev 3:5] Anyone who proves victorious will be dressed, like these, in white robes; I shall not blot that name out of the book of life, but acknowledge it in the presence of my Father and his angels.
[Deu 29:19] Yahweh will not pardon him. The wrath and jealousy of Yahweh will blaze against such a person; every curse written in this book will fall on him, and Yahweh will blot his name out under heaven.
[Deu 7:23] But Yahweh your God will put them at your mercy, and disaster after disaster will overtake them until they are finally destroyed.
[Deu 7:24] He will put their kings at your mercy and you will blot out their names under heaven; no one will be able to resist you-until you have destroyed them all.
[Exo 32:32] And yet, if it pleased you to forgive their sin. . .! If not, please blot me out of the book you have written!'
[Exo 32:33] Yahweh said to Moses, `Those who have sinned against me are the ones I shall blot out of my book.
[Deu 29:19] Yahweh will not pardon him. The wrath and jealousy of Yahweh will blaze against such a person; every curse written in this book will fall on him, and Yahweh will blot his name out under heaven.
More examples of how the Book could be considered an open book and some that indicate otherwise.
David believed that the Book of Life is an open book,
[Psa 69:27,28] Charge them with crime after crime, exclude them from your saving justice, erase them from the book of life, do not enroll them among the upright.
Indication that perhaps not all are written in the Book of Life from the foundation.
[Dan 12:1,2] `At that time Michael will arise-the great Prince, defender of your people. That will be a time of great distress, unparalleled since nations first came into existence. When that time comes, your own people will be spared-all those whose names are found written in the Book. Resurrection and retribution `Of those who are sleeping in the Land of Dust, many will awaken, some to everlasting life, some to shame and everlasting disgrace.
[Phil 4:3] and I ask you, Syzygus, really to be a `partner' and help them. These women have struggled hard for the gospel with me, along with Clement and all my other fellow-workers, whose names are written in the book of life.
This one indicates that not all are written in the Book of life. And that there are many who are not permitted entry into the New Jerusalem because of that.
Rev 21:24-27] The nations will come to its light and the kings of the earth will bring it their treasures. Its gates will never be closed by day-and there will be no night there and the nations will come, bringing their treasure and their wealth. Nothing unclean may come into it: no one who does what is loathsome or false, but only those who are listed in the Lamb's book of life.
A great deception will befall those who are not written in the Lamb's Book of Life. So that indicates that not all are written from the foundation. Yet, believers in Jesus are saved by the blood of the lamb. So their names must get written at some time into the Book of Life.
[Rev 17:8] `The beast you have seen was once alive and is alive no longer; it is yet to come up from the Abyss, but only to go to its destruction. And the people of the world, whose names have not been written since the beginning of the world in the book of life, will be astonished when they see how the beast was once alive and is alive no longer, and is still to come.
More, or amplification, of the great deception. This one confuses the issue, because it specifies "from the foundation of the world".
[Rev 13:5] The beast was allowed to mouth its boasts and blasphemies and to be active for forty-two months;
[Rev 13:6-8] and it mouthed its blasphemies against God, against his name, his heavenly Tent and all those who are sheltered there. It was allowed to make war against the saints and conquer them, and given power over every race, people, language and nation; and all people of the world will worship it, that is, everybody whose name has not been written down since the foundation of the world in the sacrificial Lamb's book of life.
Well if the book is open, and the Gospel message which is to all mankind has been heard and believed, what would prevent a drop of Jesus' blood from being added to the name of the new believer? If other than I stated above, why can't God add names if he desires? After all, it is the Father's desire than none should perish, but that all should have everlasting life.