During RT you want to cells to be sensitive to damage, especially (ideally only) the cancer cells. So antioxidants are not recommended at that time.
The fact that cancer cells are likely to use vitamin C is NOT surprising they are metabolically more active so you would expect that actually. I have a big problem with treatment of cancer cells in vitro (Petri dish). To put is bluntly this is very tricky to interpret at best and in my opinion mostly BS. Point in case, you can microwave you petri dish and kill all cancer cells and voila your cancer is cured, hardly applicable to an organism! Hell, with a fine enough needle and a microscope you could physically kill the cancer cells in a Petri dish.
After the RT treatment you are presumably cancer free and you want antioxidants to prevent unwanted DNA damage and help the immune system. So the situation is different. However there are a lot of different antioxidants that have different effects.

M