Sounds good. I usually start most of my soups using those ingredients.
Now you know the name. Yeah, it's the basis for most of the western world's soups, stocks and stews, and there's variations on it around the world.
"sauteed" is one of those occam's razor steps, depending on the recipe. Basically, you don't have to with some soups, but with others (Like Gumbo, and Jambalaya) the scorch flavors the dish. (In this case, the rice. Same with Spanish Rice, substituting tomatoes. Dirty rice, beans'n rice...)
I stuff the bird with it in stew (1.5"-2") chunks, raw, because you're going to roast it anyway. Slow cooker, any roasting method works, I've done Turkey in a Hole that way, and it came out fantastic. The point is the drippings are a concentrated turkey (Chicken, goose...) stock. Which is great for the leftovers, if any. it is now my official recipe for my Yule Goose Gravy.
Lots of substitutions here, one of my favorites is sweet potatoes/yams in lieu of the carrots. I've also use rutabega+mirepoix.