Can people with polysistic ovarian syndrome still have children?

Absolutely, yes. There are ways to increase your odds of ovulating despite pcos, either with lifestyle changes and/or medications.
Yes. The problem with pcos is the lack of ovulation, therefore, not allowing women to get pregnant. Given that there are no other reasons for infertility, including no male factors of infertility, and that weight is not an issue, there are medications that can be prescribed by a physician that can help you ovulate.
Yes. It may take longer or you may need to be treated with one of the ovulation inducing medications, but you should still be able to conceive even with polycystic ovarian syndrome (pcos). Women with pcos ovulate about 3 or 4 times per year instead of about once each month. If you are sexually active at the correct time, you can still conceive. If you are treated to induce ovulation it may be quicker.