Might there be manifestations of gastric cancer with ovarian metastasis?

If you mean a that: Stomach tumor announces itself by an ovarian mass, the answer is yes, even has a name called kruckenberg tumor, but that applies to any tumor travelling to the ovary.

Ovarian cancer: Most people do not have symptoms until advanced stages but if symptoms occur, they may include bloating, pain, early satiety (feeling full after a few bites) or change in urinary symptoms. These same symptoms occur at late stages.