How effective could a diet rich in antioxidants really be in reducing risk of cancer / tumor growth?

No definite answer: A diet rich in antioxidants is generally a plant based diet and is good for one's health. Whether such a diet will prevent or control tumors has not been established.

Avoid during tx: There has been much discussion and study on the use of antioxidants during active cancer therapy. The dilemma is that chemotherapy and radiation both work significantly by creating oxygen radicals inside the nucleus of the cancer cell and therefore causing lethal mutations in the dna of the cell, which eventually causes it to die.Thus we need oxygen radicals to kill cancer.There is controversy.