Yes, if an employer asks (and nothing currently in NY law explicitly bars them from asking although they're not supposed to do so in a manner that discriminates against a protected class), then his failure to answer truthfully is at his own peril. Frankly, I'd consider hiring someone with a criminal record, but someone who lied on an application would be immediately fired (and you probably wouldn't qualify for UI).
Certainly arrest and conviction records are trivially researchable.

