In my opinion, technically it is real, many times over. There are tons of Dollars-themed websites in which people use the sites similarly to how they would on Durarara(BBS/Chatting).
If you're looking for more of a "gang" aspect, there are a couple things to keep in mind: Dollars is based in Tokyo, Japan. All the news they post on the sites in Durarara is local, and everyone they contact is within reach despite being anonymous. In the anime, Dollars doesn't seem to be accessible to the rest of the world, especially being in Japanese and invite-only. People on REAL international Dollars sites don't bother posting in a way where they would on the anime, since you can't just tell someone to look down a street in your city, if they live in another country.
We must also keep something else in mind, and it is that Durarara is fictional. The things that happen in it, especially the supernatural elements, are not things that would happen in real life. The way people interact in an anime, and what they do, is unrealistic--- And therefore, expecting a Dollars exactly like the anime, to come into fruition in real life, is unrealistic.
Still, we have sites like Drrr and others that we can enjoy.