Is it actually true that an abdominal ultrasound will show ovarian cancer?

It might but may not. Abdominal ultrasound along with pelvic ultrasound is a good screening test to take a look at the ovaries. If the ovary is normal in size, you would know that there is not an obvious tumor in that location. But ovarian cancer diagnosis requires presence of a growth in the ovary or in the abdomen, often associated with fluid collection. Ultimately a biopsy or surgery is the only way to be sure of can.