No, sulfa drugs contain sulfur....but they are not used in the body the same way.
This link shows the amounts of elements in the body:
Oxygen, carbon, hydrogen, nitrogen for gases except carbon
Calcium, phosphorus, potassium, sulfur are the 4 most abundant non gaseous elements. Hard to be deficient in this element, IMO. So many plants have it. Eggs have it...etc.
So many of our enzymes rely on sulfur. Some amino acids like methionine and cysteine contain sulfur.
Sulfa drugs are capable of arousing an allergic reaction in the body, because of the action of antibodies to foreign invaders. Sulfites uses as preservatives may also cause reactions in sulfa sensitive people.
But sulfur itself does not. SulFATE does not.
The formation of the enzymes in the brain...glutathione, for example. There may be genetic damage or reasons for the enzymes to fail, but I don't think it is because of a lack of sulfur.