You don't need to pass a test to get a duck stamp. However, you will need to sign the Federal duck stamp across the face in ink as well as have a NYS HIP number in addition to a NYS smallgame or sportsman's license to hunt waterfol in NY state.
HOWEVER....
NYSDEC has an optional free program that is called "Waterfowl Hunter Education". It is a minimum of 3 hrs long. My waterfowl club, Lake Plains Waterfowl Association, was instrumental in starting the program many years back. I am a certified instructor. If you attend the course and pass the exam at the end of the program, you will receive a certificate which is required on certain WMA's, State Parks and Iroquois and Montezuma NWR's in Western NY in order to waterfowl hunt. Our course runs 4 hours in length and we have one of the highest passing rates in the state. This year, we held a total of 5 courses in addition to a youth course this coming weekend. I recommend this course to all NYS waterfowlers as the course covers identification of restricted species, bag limits, regulations, waterfowling ethics, boating and gun safety and ballistics. It is to your benefit and to the resource to take this course.