If a woman doesn't do a papanicolaou in 2 years, is that still fine?

Yes, if low risk . The new protocol for pap is every 3-5 years for people without risk factors, such as history of multliple partners, previous cervical disease, abnormal pap smears, positive high risk human pappiloma virus, etc.
No . Usally in sexually active woman the recommendation for yearly papsmear.