Does some of this take place after the Saints book was published?

If you want to get technical then yes. The book was published in 2003 and the present day portions in the movie are in 2005.

The movie isn't really a direct adaptation of Dito's life/book, it's more inspired by them. The characters are all combinations of various people he knew. For example, Giuseppe and Mike are shown being killed off but their real life counterparts lived. The reverse is true of Laurie, who had died of AIDS before Dito returned to New York but of course is alive and well in the film. So Dito was more about making a good story rather than a recreation of his life.