Are the chances slim of having a child after developing polycystic ovary syndrome?

Most can have child. Polycystic ovarian syndrome (pcos) is common, affecting 8-10% of women. Some with pcos have infertility. Most women with pcos can have children. Some conceive with no fertility treatment, some need medications like metformin, Clomid (clomiphene) or Femara (letrozole), while others need in vitro fertilization (ivf). Pcos women often respond better to fertility meds. See a fertility md if you want to have kids.
Not slim. The rate of infertility in women with pcos range from 40-80% depending on the study you look at. With that being sad, having pcos does not imply you can not conceive ! you can have normal ovulation despite having pcos as its really a spectrum with various degrees of "severity". Eat healthy, exercise and try to avoid bpa ( canned soups, plastic bottles). Talk with your doctor and good luck.
No. There is a very good chance to get pregnant after a diagnosis of pcos sometimes spontaneously or commonly with a large number of interventions available.