@Ampere0
You should worry. A lot.
I think you should try to talk to someone who knows the implications of this, but I’m afraid that you are about to get a roommate you will never be able to get rid of.
Even if NY did agree to pay you, they wouldn’t pay your regular fee. You would probably be subjected to inspections and other forms of harassment as well.
You can write a letter for this person but make sure that you tell the whole truth about the situation. He might be attempting to perpetrate a fraud.
Or you can just tell him you wrote the letter and hope he leaves when the benefits are not forthcoming.
He should be applying for housing through HUD or whatever they have in NYC, not through you.
NY has some really strict laws regarding housing and they are not there for the benefit of landlords.