To the best of the information available it should.
The Statue Cruises does accept New York Pass as a ticket option as it is listed on their site. And if you click on Book Now it will give you an option to reserve seating on either the Battery Park Ferry or on the Liberty Park Ferry. You can also see the same mentioned in their FAQ which allows you to enter from one side and leave to the other.
Though I would question the wisdom of buying a New York Pass and going to Liberty Park in NJ to go to the Statue of Liberty or Ellis Island.