The answer depends on the verbiage in Non-Compete Agreement, the labor laws in that state in the state of New York enforcing non-compete means paying your former employee his/her salary. In the state of Indiana I know that a person was forced to close the business that was a direct competitor of his former employer. In Texas I see it being enforceable similar to what was done in Indiana.
But in general this is a question for lawyers. If you are planning to go after someone you will have to retain one anyway and if someone is going after you will require the exact same thing.