They give a very good impression of the setting, and they also give a pretty good background for understanding how the rules work.
The game was designed to very closely emulate the fiction of the books (Evil Hat and the author worked closely together for about a decade, and much of Evil Hat's work on developing and refining Fate over the years and multiple products has been intended to get "good enough" to do the Dresdenverse justice), and knowing the fiction will help understand much of the game design, especially the magic subsystem and the overall "feel" that the game's rules engender.
Another point in favour of reading the fiction is that the rules as presented are not exhaustive – the rules give you lots of leeway to come up with your own character templates, creatures, rituals, and the like. Having read the books will give you more of a grip on the world so that you can more easily make stuff that enhances the game.
I would say that reading one or more of the novels is strongly recommended, but not strictly necessary. You can still enjoy DFRPG a lot without knowing the books, and the rules do come with a lot of embedded flavour (especially if you also have Our World), so you can absorb sufficient fiction from the rule books alone.
That said, if you are getting the RPG in order to pick apart and understand Fate, it's not necessary to read the fiction. DFRPG is an excellent instantiation of Fate, and as I understand it, is the closest incarnation to the next generic version of Fate in Fate Core. However, even then you'll understand the raison d'être of much of the rules better if you know at least something of the fiction it is inspired by and attempting to support.