Save meat from chicken broth?
Edible? Absolutely yes.

Flavorful?  ....you should taste it and tell us.  Seriously, don't serve a meal to anyone, yourself included, until you've tasted it and it tastes at least decent.  (Not trying to be snarky here, that's literally the best cooking tip I was ever given)

Nutritious?  Probably somewhat--that chicken muscle is primarily protein after all.

Generally, soups are made with bones because bones can't be used for anything else, so it's more economical to get soup-flavor from bones (making the stock), then use meat for texture and to add variety to the liquid.  I was taught to put meat into soups in the last hour of cooking.  Many recipes I've seen call for taking out the whole pieces of meat and shredding it or pulling it before serving it in the soup.