Remember that yeast fermentation creates sulfites- It is impossible to make a sulfite-free wine, because wine yeast produce sulfur dioxide (SO2) during the fermentation process. Wines with no added sulfite contain from 6 to 40 ppm of sulfite. Some winemakers add sulfites to protect the wine, but even then at 50 ppm or so, it's less sulfite than is in a package of dried fruit like raisins, or a food like prepared horseradish. Wine headaches don't come from sulfites, although that's what gets the blame much of the time.
Even beer often has sulfites, because of the fermentation process.
In any case, if you are using sulfites to neutralize chlorine, it's a chemical reaction so that there aren't sulfites in the water once it's mixed and it's an instantaneous reaction.