A spur on a line that is hardly ever used is pretty ludicrous. I take it you are referring to the Stewart airport connection which is already served by ShortLine and the Port Authority.
There is no viable right of way to get to the airport from the existing tracks. Random developments have blocked any route that splits after Salisbury Mills/Cornwall. Good luck buying those out even if the topology is favorable for rail right of way. One can try using the I-87 right of way splitting from the existing route before Salisbury Mills/Cornwall, but in places the residential development seems so close to the highway that I doubt that there is enough width for the tracks and the eventual 3 lanes each way highway. Interestingly enough there is an existing rail freight spur ending just south of route 94 that might take you into the city of Newburgh, passing through New Windsor, that might actually provide some ridership to justify some investment. Most likely though the idea is to create a big parking lot at Stewart and count that as the Newburgh station. Even though that is Newburgh, I doubt there is any place for a big parking lot downtown.
For maximum bang on the buck, if the MTA is ever hoping to get any spur to Stewart, the yard should be south of the split of the rail right of way and the I-87 right of way. That unfortunately is east of substantial portion of the current ridership.