Should a 23 yr old woman have a "papanicolaou" done even if she hasn't had intercourse ever?

Yes, she should. Yes, accordint to most protocols, she should. However, personaly and theorectically, probably not, for the risk of cervical dysplasia/cancer is extremely low. Clinically, the health provider can only document a patient reports no intercourse ever, but the actually situation may be different.
No. Papsmear should start after the intiation of the intercourse at any age after starting the sexual intercourse.