I'm not familiar with that book, but my experience has been that at first the going is slow but then it becomes much better, so if you're willing to slog through the early stages, you'll be fine. The syntax rules are pretty much the same as Attic and I'm sure the book would point the few differences -- and in fact the sentence structure in Homer is easier than what you typically get in Attic works, although the fact that it's poetry can obscure that at times. There are differences in the inflections, but my main problem was the number of inflectional alternatives, especially with the pronouns (and of course, learning the vocabulary). But once you get used to it, and it's similar enough to Attic that you can pick it up as you go, it becomes much more reasonable.
There's also an edition of the first book of the Iliad by Draper, which is designed for people in your position, who want to go from the Attic they know to reading Homer. It's very thorough, so you might want to take a look at it as well.