The book does tell you quite a lot about Haytham, but writing-wise, it is... not good, and there are places where you feel the book's and the game's Haytham are two different characters (his feelings towards the Assassins and the Templars, for example), so be warned.

The Haytham in this story is... kind of a hybrid between the two. I am taking the book into account only when what it describes doesn't contradict what we see in the game.