Short answer, Yes! I hope the following is helpful!
This citation is not from the law directly but from the NYS RPA.
Your home county restrictions apply, so if you have full concealed carry, no worries!
A non-resident citizen may possess a rifle or shotgun in New York, as long as it is unloaded while being transported. No person may carry, possess or transport a handgun in or through the state unless he has a valid New York license. New York does not issue licenses to non-residents nor does it recognize licenses issued by other states. (A provision of federal law provides a defense to state or local laws which would prohibit the passage of persons with firearms in interstate travel. If a person is traveling from any place where he may lawfully possess and transport a firearm to any other place where he may lawfully possess and transport such firearm and the firearm is unloaded and in the trunk. In vehicles without a trunk, the unloaded firearm shall be in a locked container other than the glove compartment or console. Necessary stops, e.g., gasoline and rest, seem permissible.) A member or coach of an accredited college or university target pistol team may transport a handgun into or through New York to participate in a collegiate, Olympic or target pistol shooting competition provided that the handgun is unloaded and carried in a locked carrying case and the ammunition is carried in a separate locked container. An alien may possess a rifle or shotgun for use while hunting provided he has a valid New York hunting license. "If such (handgun) license is issued to an alien, or to a person not a citizen of and usually a resident in the state, the licensing officer shall state in the license the particular reason for the issuance and the names of the persons certifying to the good character of the applicant." Non-resident target shooters may enter or pass through New York State with handguns for the purposes of any NRA approved competition if the competitor has in his possession a copy of the match program, proof of entry and a pistol license from his state of residence. The handgun must be unloaded and transported in a locked opaque container."
And just in case you need to travel through NYC to get to LI:
A NY permit issued outside of NYC is NOT valid in NYC, unless
you obtain a NYC certification, in essence you apply for a NYC
permit also. A NYC permit is good statewide. A non-NYC permit
holder may transport his guns through NYC if they stay in a locked
container, and there are no stops in the city on the trip. This is
by state law, the same effect would be had under the federal law
also. A permit holder may also buy a handgun in NYC, and legally
transport it out. (NYPL 400.00(6))