As you are probably familiar, Westchester, Newburgh, and Islip support a lot of traffic to east coast and midwest hubs. People tend to use these airports to avoid the hassle of LGA, JFK, and EWR--they want nothing to do with them, in fact. The only plausible market would be as a flight crew shuttle service.
The air taxi thing is nothing new. Many top executives, today, use helicopters to get around the city and commute home. Fact is, they go right to the lower manhattan piers. I don't think you could make any money with scheduled 402/406 service today from congested airports to outer airports. Unless you can come up with a somewhat cost effective scheme to get people to the city center, a commuter network such as the one you suggest probably won't make it.
In the 1970s, New York Airways used helicopters to shuttle people around to connect to Pan Am flights, etc. This high density air network has spawne ideas such as the CH-47 passenger variant, the FAIREY-ROTODYNE, and now they are talking about the V-22 Osprey Civil variant. In reality, metro air service on a large scale just has not caught on.