No. You may file a NY state tax return by mail.
Per the following link, https://www.tax.ny.gov/pit/efile/efile_mandate_for_individuals.htm:
"You're required to electronically file your return if you meet all three of the following conditions:
- you use software to prepare your own personal income tax return;
- your software supports the electronic filing of your return; and
- you have broadband Internet access."
However, if the software does not allow you to e-file, the second condition has not been met.
Further, the New York Department of Taxation and Finance removed the penalty so you may file a NY state tax return by mail (see page 35: https://www.tax.ny.gov/pdf/current_forms/it/it201i.pdf). Please review the following TurboTax FAQ for more information:
https://ttlc.intuit.com/replies/3302166
