Crumble the sausage into a 10- to 12-inch frying pan over medium-high heat. Stir often until sausage is lightly browned, about 5 minutes. Using a slotted spoon, transfer sausage to a large bowl.
Discard all but 2 tablespoons fat in pan. Add onions to pan and stir often until limp, about 5 minutes. Add onions to sausage.
Add celery, cornbread, apricots, cranberries, eggs, sage, and butter and stir to mix well, adding just enough broth to lightly moisten dressing.
Spoon dressing into a shallow 2 1/2- to 3-quart casserole and cover.
Bake in a 325° oven until hot, about 25 minutes (if chilled, 50 to 60 minutes). Then uncover and bake until top is lightly browned, 15 to 25 minutes more. Add salt and pepper to taste.