"Is this acceptable?" - yes, but it's a lot of work. You have to enter your federal return first, then enter NY.
"Is there a penalty?" - no, but you will have to pay the full fee for federal and state (if any) with TurboTax.
"Do I need to attach a copy of my Federal return that was e-filed?" - yes, if you print and mail your NY return, you will need to print and mail a copy of the federal return with the state return. This is why it will be critical that the federal return in TurboTax be identical to the one you e-filed previously.
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