When growing soybeans specifically as a cover crop, can you still harvest the beans?
If not, why bother with soybeans rather than vetch, clover or similar since these can fix more than twice as much nitrogen?
To get the most benefit from a green manure crop it needs till be tilled under prior to pod set. So to answer your question no. When pods are set the excess Nitrogen store by the plant is being converted into seeds. On why not plant vetch, clover or similar legume the answer is you could and they do produce much more nitrogen but vetch and clover are cool season legumes and do not do well in the summer unless you have short cool summers. If you have long hot summers southern peas would be a better choice vice soybeans also velvet beans is another good choice. If nitrogen is not as important and want good bio mass on a green manure buck wheat is a good choice also again for cooler areas rye. Rodger
Here is a link that might be useful: cover crops
Is the object is to increase soil fertility, and not to grow grow something edible? Vetch & clover do fix more nitrogen, and can add a lot of organic matter as well. But heresy though this is... if the object is soil enrichment only, then turn the soybeans under in the green shell stage. The seeds will rot, releasing a great deal of nutrients, including nitrogen. Peas & beans would do the same thing. I just couldn't do it, it runs against all my instincts as a gardener. ;-)
Of course, the advantage of growing edible legumes for cover crops (I like the term "green manure" better) is that you get a little food as well. And while the nitrogen released by turning under mature plants is not as great as that of the earlier stage mentioned by Rodger, the nodules will still release nitrogen as the plant decays.
My recommendation would be to pick a little edamame before you turn the soybeans under. The plant is still mostly green at that stage, and will decompose more quickly than if the seed were allowed to dry. Save the vetch & clover for the cool season, if your growing season is long enough for you to do so. Or grow English peas in the cool season... and eat a few of them as well.