Gypsum is bad news for a number of reasons including that it doesn't work in breaking up clay as claimed.Over application cause deficiencies in a number of antagonistic nutrients.
Gypsum will only "help" soils that meet given criteria. If you have a heavy clay soil, and that soil is poor in calcium and rich in small monovalent cations (like sodium)... then gypsum will make the soil more friable.
Naturally, it won't necessarily improve the soil ecosystem (beneficial fungi like mycorrhizae, helpful bacteria, helpful creatures like earthworms) and over application would probably hurt all of those. Plus, if you add a ton of a few cations and anions... the net effect is to decrease the availability of other "similar" ones (and plants need an assortment of cations...).
Adding bulk organic material is better, but it takes more work, and more material. If what you are adding hasn't been broken down then (during the process of it breaking down) the net available nitrogen in the soil will decrease. If it has already been broken down it can only increase the available nitrogen. If you tilled in wood chips or bark (for example) the nitrogen would go down as they were chemically decomposed. But if you added coffee grounds (which are already chemically "broken down") the nitrogen would go significantly up (because they have a lot on N).