No.
A quick google finds this
report by the US Census Bureau. According to the report, in 2011 739,000 people hunted in New York State. However, there were too few hunters in MSAs larger than 1,000,000 people to calculate what percent in MSAs over 1,000,000 participate in hunting. That makes it seem pretty rare in NYC.
Also, hunting is pretty unheard of here just anecdotally. I've known a few people who hunted when they were kids back in real America. But, I've never met anyone that goes upstate to shoot deer.