The purchase of a rental home here would be viewed as an "investment property" purchase. While you would not qualify for a residential mortgage in the formal sense, you may qualify for an investor or commercial mortgage - in which case you may be expected to put at least 25-30% down and accept a slightly higher interest rate than if you were going to occupy the home.
If you are asking about this from the stand-point of a "first-time buyer", then I would have to say honestly that I am not 100% sure, but I would not imagine that an investor who could afford to own an investment property could then later qualify or benefit from any purchase incentives that might normally be offered to a true first-time buyer who will occupy the house. Once you own this investment property - you are an owner in the state of NY. I don't think you could then qualify as a "first-time" owner occupant on a subsequent purchase.
As to qualifying as a resident the answer is "NO"! You would have to pay taxes but you would file as a non-resident, per Katie Torello of KMT Books.
Thanks for a great question and please be in touch if you need further assistance. Ithaca does have a number of successful absentee owners who do rely on a network of property managers and other professionals to assist them - I'm sure you could do the same if you were so inclined.