There are about 3.4 million housing units in NYC and a reported 42,000 AirBnB listings = 1.2%. Some 19,000 of these are private room/share (according to AirBnB) so that leaves about 0.7%.
As a portion of these are renters/owners renting out their primary residence the actual number of commercial operators will be only a subset.
So pretty difficult for it to have any significant impact.