No, that is not correct. As you can see below from the instructions for Form IT-370, that a federal extension form is no longer accepted for the New York extension.
General information
Purpose – File Form IT-370 on or before the due date of the return to get
an automatic extension of time to file Form IT-201.
Note: We no longer accept a copy of the federal extension form in place of
Form IT-370.
You can file a New York State extension by using the online link here: NY Apply For an Extension
