Absolutely not!

Puzo, for whatever reason, simply left out the name (and description) of one of the New York Families. The novel explains that there were to be representatives from ten other Families besides the New York Five Families. Only six of them were identified (Carlo Tramonti from Florida, Joseph Zaluchi from Detroit, Frank Falcone from the movie unions on the West Coast, Anthony Molinari from San Francisco, Domenick Panza from Boston, and Vincent Forlenza from Cleveland). The fact the other four Families weren't described doesn't mean they didn't exist. So it is with the "missing" New York Family.

Its been stated before, and now worth repeating - (from the novel):

The arrival time had been staggered for between nine-thirty to ten A.M. Don Corleone, in a sense the host since he initiated the peace talks, had been the first to arrive....

after a few pages of describing the out-of-town Dons, Puzo added:

The representatives of the Five Families of New York were the last to arrive and Tom Hagen was struck by how much more imposing, impressive, these five men were than the out-of-towners, the hicks. The five New York Dons were stout, corpulent men with massive leonine heads, features on a large scale......

Puzo clearly made a distinction between Vito Corleone and the other five Families. He wrote that Vito had arrived first, and later the five New York Dons arrived.

I cannot even offer a reason why Puzo didn't describe the fifth Family, but that descriptive omission doesn't mean the Family didn't exist.

In short, there were five New York Families PLUS the Corleones.