No, and this is the most common mix-up on the label. Sulfite preservatives (E220 to E228, such as sodium metabisulfite) are reduced sulfur compounds that release sulfur dioxide gas, which is what provokes wheezing and flushing in sulfite-sensitive asthmatics. Sulfate is sulfur already fully bound to oxygen. It is chemically stable, releases no sulfur dioxide, and is the same anion you get from tap water and from magnesium sulfate. If sulfites are your trigger, ammonium sulfate on a bread label is not one.

Because the same salt does two unrelated jobs. Ammonium sulfate is a nitrogen fertilizer for the same reason it is a yeast nutrient: yeast, like a plant, needs usable nitrogen to multiply. What is on your bread label is food-grade material at a fraction of a percent of the flour weight, most of it eaten by the yeast during proofing, and it is regulated separately from the agricultural grade. The shared name is doing a lot of viral work that the chemistry does not support.

Three things at once. It supplies nitrogen so the yeast reproduces fast and on schedule, it buffers the pH drop that comes as the yeast turns sugar into carbon dioxide, and it tightens the gluten network so the dough is extensible without tearing on high-speed mixing and shaping lines. None of these are needed in a slow-fermented loaf, where time and flour do the same work. That is why you find it in bagged sandwich bread and not in a bakery sourdough.

It is usually excluded on those protocols, since they cut added sulfate salts along with high-sulfur foods. Worth keeping the scale in view though: the amount in a slice of bread is small next to eggs, cruciferous vegetables, garlic, onion and sulfite-preserved dried fruit or wine. If you are trialling low sulfur for hydrogen sulfide symptoms, tackle those first and treat the bread additive as a late refinement rather than the starting point.