In each menstration cycle, follicles grow on the ovaries. Eggs develop within these follicles, one of which will reach maturity sooner than the others and be realeased into the fallopian tubes hence ovulation. With polycyctic ovaries, the ovaries are larger than normal and they a basically undeveloped follicles which appear in clumps rather than a bunch of grapes.
Women with PCOS will have polysystic ovaries because PCOS is a syndrome, it is just a name given to the metabolic conditon in which women will polycystic ovaries along with other symptoms. PCOS is a dysfucntion which affects ther entire body not just the ovaries. So yes a woman can have PCOS with out having any cystic on her ovaries.