In someways, this is a chicken or the egg sort of deal. The airlines aren't going to use it unless there's sufficient customer demand and an easy way to get there.
Customers aren't going to use it unless there are airlines there that have flights to destinations they want to go to.
This airport is too far north for most people in the region to want to use. It will probably best serve northern Westchester, Putnam, Duchess, Orange, Sullivan and Ulster. These are places with heavy car ownership levels and which I don't see any convenient rail routing for most of them.
It's the same problem down on Long Island with Islip Airport. I love using Islip becasue its cleaner, less busy, the security people are friendlier, unfortunately the only carrier in there nowadays is Southwest, Delta and Continental pulled out a few years back. That's more a discussion on airlines than trains tho.
Looking on a map, theres already a Metro North station nearby, Salisbury Mills-Cornwall and on the Hudson line across the river theres nearby Beacon station. It seems like a better idea to run hourly airport shuttles timed with the trains, similar to what they have at Islip airport for the LIRR.