Yes. The book of life implies a conscription or a knowledge of those chosen to life because the life of glory is an end exceeding human nature.
The divine life, even considered as a life of glory, is natural to God; whence in His regard there is no election, and in consequence no book of life.
The life of grace has the aspect, not of an end, but of something directed towards an end. Hence nobody is said to be chosen to the life of grace, except so far as the life of grace is directed to glory. For this reason those who, possessing grace, fail to obtain glory, are not said to be chosen simply, but relatively.
Likewise they are not said to be written in the book of life simply, but relatively; that is to say, that it is in the ordination and knowledge of God that they are to have some relation to eternal life, according to their participation in grace.