I wouldn't anticipate it sudsing but it's not altogether possible to predict the reaction. Watch closely, if it's foaming, drain it before it drains itself onto the floor.
I also wouldn't anticipate an oxidant being any advantage in a dishwasher.
I wouldn't have anticipated that Oxyclean would attack fabric like sodium hypochlorite, since the commercials imply that it doesn't. But I demonstrated that it does, using a high-wear all cotton martial arts uniform. Bleach destroyed my first one and Oxyclean destroyed my second one, just a little slower. I know it was bleach and Oxyclean destroying them, because I used them only on the legs (which got stained from rubbing on mats) and that's where the fabric weakened to the point of failure. My third gi I used neither and it shows no such sign of failure.