ULSD should not affect a 2000 vehicle. However, you will want to use a quality additive to compensate for poor lubricity of these fuels. That applies to all diesels, not just your TDI. You will need to pass OBDII emissions, which means they will plug into the diagnostic connector during an inspection. If you don't have a check engine light on you should pass. As stated earlier after a certain number of miles NY considers the car to be used and you can register it whether it qualified for NY emissions when it was new or not.
Good luck with the car, I think you're going to like it. My '98 TDI gets 53 MPG on the highway. Local it gets a measly 42. Although I wouldn't expect that from a newer one.