Only if there is something else more reactive present in the wine. That's the rationale for adding sulfites: they react with oxygen faster than the phenolics do. But even sulfites, with time, will oxidize the phenolics, because of the energetic favorability of doing so. This could be prevented, I suppose, in the same way that Miller Brewing Co prevents photochemical decomposition (aka "skunkiness") of Miller High Life (thereby allowing them to bottle it in clear bottles, as opposed to the amber used by everyone else): add enough sodium borohydride (a potent reducing agent) to reduce everything in the wine. This is one of those clearcut cases, however, where one can argue that the cure is worse than the disease, as anyone who's tasted Miller can attest.
Mark Lipton
(posting in the aftermath of a rabbit and Volnay meal)