The short answer: her periods will probably be irregular when she stops taking birth control, unless she's taken other measures to reduce her PCOS symptoms.
Source: I'm a medical student who has PCOS.
The long answer: While on birth control pills, menstrual cycles are entirely controlled by the pills. This means that if the patient takes the pills religiously, their menstrual cycles will be regular, with their period happening exactly when specified by the pills. PCOS is a complex disease with many underlying factors, including genetics and lifestyle (e.g. obesity). Many of its symptoms, including acne and irregular periods, can be controlled by birth control pills, but the underlying genetic issues will still be present and often the underlying lifestyle issues will still be present. Therefore, when a patient with birth control pills stops taking the pills, if they have not done anything else in their life to reduce their PCOS, it is likely that their former symptoms will return. This means if they previously had irregular periods they will probably get irregular periods again.
The exception would be if they have made some kind of lifestyle change to reduce their PCOS, such as losing weight. Weight loss can normalize hormone levels and help with PCOS symptoms (e.g. "most treatments of obesity...achieve modest reductions in weight and improvements in PCOS phenotype", see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3649566/). Weight loss can sometimes restore fertility in PCOS patients who have lower fertility due to PCOS.
Here's my personal experience: I had PCOS, diagnosed by an endocrinologist via an ovarian ultrasound, clinical history, and blood tests. My periods were EXTREMELY irregular. I had a normal BMI but it was on the "high side" of normal. I learned in medical school about how PCOS is tied in with sugar consumption (high sugar consumption -> high insulin -> higher androgens -> worse PCOS, e.g. http://imaging.ubmmedica.com/CME/pt/content/p010531a.gif). I also learned that consequently PCOS is sometimes treated with metformin, a diabetes drug. Instead of taking a drug, I eliminated white and brown sugar from my diet and limited myself to an appropriate number of calories per day. I also exercise for an hour a day. Consequently, I lost 25 pounds (current BMI = 20, which is low end of normal) and my PCOS symptoms have entirely vanished: I have clockwork periods, and a recent ultrasound of my ovaries showed no cysts, so I no longer meet ANY of the diagnostic criteria for PCOS. Because I have "cured" my PCOS through lifestyle changes, as long as I continue the lifestyle changes I am "cured" of PCOS. In contrast, I know someone who is taking birth control pills to hide their PCOS symptoms, and if they stop taking the pills their symptoms do come back. Note - everyone is physiologically unique, and so people respond to lifestyle changes to a different degree. Diet and exercise are great, but may not always "cure" someone - the best resource is to talk to your own physician.