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 23 year old date a 17-year-old in New York?

The age of consent in New York is 17. Thus, if you are 17, dating someone who is 23 is not unlawful.

Can a 17-year-old sleep with a 25 year old?

Thus, sexual relations between two 17-year-olds would be illegal, as would relations between a 17-year-old and a 25-year-old.