If she takes birth control pills then are the sugar pills as effective at preventing pregnancy as a placebo effect?

No: The "sugar" pills are there to maintain a regular dosing schedule. Once the 3 weeks of active pills are finished, the hormonal trigger for menstruation occurs, & a period will follow. The "placebo" pills have nothing to do with the period other than to keep the schedule on routine. But one can't get pregnant during the period, so pregnancy is still prevented even though the pills are not active.