Did Baba from The Kite Runner die before Amir published his first book or after?

Baba does not live to see Amir publish his first book.  He does, however, develop an appreciation for his son's talent in the days before his death.

Baba had always scorned Amir's interest in writing.  To him, it was not a manly pursuit, and it frustrated him to see his son engaging in the activity when he would have preferred to see him taking part in pastimes like athletics, which, in his mind, were more befitting a boy's pursuit.  Amir had always known that Baba disapproved of his literary bent, and felt inadequate and unloved because of this.  When he was a child, a family friend, Rahim Khan, had given Amir a fine leather-bound notebook.  In this notebook, Amir began to write the stories of which he was so fond and proud.  In his stubbornness, Baba had been unable to even feign interest in his son's writings; after an initial and especially hurtful rejection by his father, Amir shared his work with Rahim Khan instead.

When Amir graduates from high school in America, he finally stands up to his father and tells him that he is going to be a writer.  Baba is not happy about his decision; he would much prefer to see his son pursue medicine or law.  Amir is firm, however, and Baba has little choice but to let his now-grown son pursue his own destiny.  Happily, Baba mellows as he grows older, and as a result of the loving care he receives from Amir and his new bride Soraya during the last days of his life, he at long last develops an appreciation for his son's talent.  As Baba lies on his deathbed, Amir discovers his precious leather-bound notebook in his father's possession.  Baba weakly tells Amir that he had asked Soraya to bring it to him, and says, "I hope you don't mind" (Chapter 13).