If I try and meet a person who I believe is underage, but that person turns out to be an undercover police officer can I be charged with a crime in New York?

Yes. In the area of rape, other sexually related crimes (LINK), or child pornography (LINK), law enforcement will often act in an undercover capacity to establish relationships with people online.  If you meet someone you believe to be underage for a sexually related purpose, in New York you can be charged with Attempted Rape or Attempted Criminal Sex Act, or federally you can be charged with Coercion and Enticement of a Minor in violation of 18 U.S.C. 2422(b).