The "Fables" series is published by Vertigo, which is part of DC Comics. Does it mean that they live in the same world as DC superheroes? I know that once upon a time Superman fought with Dracula, and the latter COULD be a Fable (or not... depend how do you look at it) and other characters from Vertigo - i.e. Constantine from "Hellblazer" do live in the same world (Constantine was asked could he stage fight between Swamp Thing and Superman for example).
My answer would be no. Books published by Vertigo are not necessarily considered to be a "shared universe" in the same way that the regular DC books are. (This can get extra confusing because SOME Vertigo books DO seem to share the DC Universe--Constantine/Hellblazer, as you mentioned, as well as Black Orchid and, arguably, Sandman--while many Vertigo books clearly do not share that universe, such as Scalped, Sweet Tooth, and American Vampire.) Fables would seem to fall into the category of Vertigo books which take place in their own, distinct universe, entirely separate from the DC shared universe which houses the current versions of DC superhero characters such as Superman and Batman.
As an interesting side note, it's never made entirely clear in Fables (at least not in any of the issues I've read, which is far from all of them) exactly how one qualifies as a "Fable". Many of the Fables, such as Snow White and Cinderella, originate in "fairy tales" which grew out of oral histories that have been told in various versions for hundreds of years. But some of them come from much more recent stories--characters from the Oz books and the Narnia Chronicles are mentioned, for instance, and those books have been around for less than a century (slightly more than a century in the case of Oz, but close enough). So, while it's clear that the Fables aren't inhabiting the universe of the DC superheroes, it's not inconceivable that superheroes, including the DC superheroes, might exist somewhere in the Fables universe--after all, Superman has been a "folk hero" and the subject of countless stories since the 1930's, and that's longer than the Narnia Chronicles have been around.
It's very inclonclusive. New York and LA have both come up in DC proper. And Morpheus and Daniel (Sandman) which is also Vertigo IS part of DC proper and has interacted with Constantine, Lucifer, Swamp Thing characters, Martian Manhunter, Mister Miracle, Batman, Superman, Justice League of America, Doctor Destiny, Wes Dodds, Arkham Asylum, ect...