Cereal rye grass is going to add organic matter to the soil. It's also better than leaving the land barren. The rye doesn't, however, add any nitrogen; but, it's actually better at adding the organic matter than the lugumes (beans, peas, vetches, lupines and clovers). The concept of green manure crops is to grow it thick (which also helps supress weeds), and before it goes to seed mow it or plow it under.

And, correct in your assumption regarding the peas. These lugumes add nitrogen to the soil.