I've used a pinch of cinnamon in my mash on many occasions. Reminds me I need to replenish my supply of cheap cinnamon for brewing (for cooking Saigon Cinnamon is the way to go!). The flavor/aroma has never carried over into the finished product. Not sure how much affect it actually has on reducing oxidation. My recollection is that Charlie picked up this trick when he observed a Belgian brewer using cinnamon in the mash. FWIW, I don't usually have issues with oxidation in my beers. I don't worry too much about HSA when I'm brewing, either.
As a judge, I find that oxidation is the single most common problem in beers entered in competition. Who knows, perhaps a pinch of cinnamon in the mash could give your beer an edge.