Can confirm, white souls get added, as does the section on talents, but black souls do not. I bring up talents because when you get the book, the 'medium' entry is unlocked, but it has a link to the 'talents' page, which isn't unlocked.
Another thing, atleast on mobile, you cant access the book from in game, only the main menu, which feels a bit off, but other than that, I enjoyed it. Maybe a notification in the corner telling you when you've unlocked a new entry, or one has been updated, would be nice, as I honestly didn't think to check again, but that could just be me.