Per the New York Tax preparer e-file mandate web page:
If you can't electronically file the return because it's not supported by your approved e-file software or it can't be filed on our Web site, then you aren't required to e-file it.
Additional information for preparers is available on the New York State website:
Penalties for both Preparers and Individuals are outlined on the New York website E-file - mandate for business taxpayers:
Penalties for failing to electronically file
If you or your preparer are required to file a tax document electronically and instead file on paper, you're subject to the following penalties:
In addition, any overpayment claimed on a return that was required to be electronically filed won't be eligible to receive interest until the document is filed electronically.