The legal answer is yes they can. While no criminal charges could be brought, as the age of consent in New York is 17, the parents of the 17 year-old are still free to use whatever legal methods at their disposal to prevent this

Can a 21 year old date a 17-year-old in NY?

In New York, if you are 21 years old or older and have sex with someone under 17 years old and the close in age exception does not apply, then that can be considered a criminal sexual act in the third degree which is a class E felony.