Yes, as a part of detox both aspargus and beets would be great. Definitely part of my diet.
I have also found barley grass and wheat grass juice helpful when detoxing. Clear the skin very fast.
I still would advice to take magnesium, vit C, B and selenium in addition to the greens/juicing. As a bare minimum to support high doses of iodine. And salt too, for the bromide. Boron for the fluoride.