Yes, and New York is the one state in this series where the answer doesn't depend on having a ticket at all.
The reason is the mandatory discount. Complete a DMV-approved course and New York requires your insurer to cut 10% from your liability and collision premiums for three years. New York's average premium in our data runs over $4,000 a year, and while the discount applies to the liability and collision portion rather than the whole bill, 10% of most of a New York premium for three years comfortably runs to several hundred dollars, often approaching four figures, against a course costing $24 to $60. That's why the steady-state New York move is a course every third year as a standing line item, clean record or not. Few purchases anywhere reliably return ten times their price by state mandate.
The ticket-driven version stacks on top: up to 4 points reduced, once every 18 months, applied to violations in the prior 18 months. Worth it for a driver whose total is climbing; irrelevant to a clean record, which loses nothing, because the discount pays either way.
The honest limit: nothing here shields you from the ticket itself. The fine, roughly $183 on a typical ticket in our data, and the conviction stand, and your insurer sees them. New York's course softens the aftermath; it never prevents it.
Approved courses are compared on the New York page; both benefit clocks are on our frequency page.