Will an hsg show any ovarian or uterine cancer?

Possible: A hystosalpingogram is an x-ray taken while radioactive dye is pushed through the uterus. It is definitely not a screening exam for either uterine or ovarian cancer. However, if your radiologist or physician were to see an abnormality on the exam, they would report/investigate the lesion. If you're worried about these cancers, talk to your doctor about your risk factors.

Not its main job: It primarily provides a structural road MAP of the pathway within your uterus (hystero-) and fallopian tubes (salpingo-). Ultrasound or ct scan are better modalities for looking for solid organ (/extra-luminal) abnormalities.