Legal Question in Criminal Law in New York

Probably not. Belatedly realizing you might have had a valid defense ordinarily would not justify withdrawing a guilty plea.

Besides, the lack of a Miranda warning is not a get out of jail free card. Even without your guilty plea, all it would do is to prevent the prosecution from using against you any statements you made in response to police questioning while in custody. All other evidence will still be usable. If you weren't questioned while in custody, then the lack of Miranda warnings would be irrelevant. And even if you were questioned, there might still have been enough untainted evidence to convict you had you gone to trial.

Maybe. If your statement led to your plea of guilty and without the statement you could have beaten the case and your attorney did not advise you of a valid defense, you may get the plea withdrawn as a result of ineffective assistance of counsel.