Could an abdominal/pelvic CT scan without contrast (ordered for ureteral stones) detect ovarian cancer also?

MAYBE. Although a contrast-enhanced ct--or, better still, a pelvic ultrasound--are preferred methods for visualizing the ovaries, a non-contact ct would likely show nonspecific irregularities of the ovaries. Bottom line: pelvic ultrasound is the best choice for visualizing ovaries.
Sometimes. A ct scan will show the ovaries in the pelvis. Only significant and sometimes advanced changes of ovarian cancer such as excess fluid in the pelvis may be noticeable.
Not necessarily... Seeing ovarian cancer or not from ct without contrast is less desirable and accurate. But if an ovarian cancer is big and calcified, it can be easily suspected as how it may look. But, following the specific ct protocol for a specific suspected tumor so to have better visualization and diagnosis is highly recommended. Detail? Ask radiologist.