I say go for it. Also if you have any onion, use that, and if there is any broccoli or canned or frozen corn, add a veggie to the sauce as well. Or not. This isn't quite tradtional, but to me it sounds good. Use what you have. I think Alfredo sauce, like stroganoff sauces are quite rich in flavor, so I tend to eat less and I am full up. So it stretches your meals out as well.
Stew the chicken quarters in some water with a little onion S & P and whatever herbs are on hand. Save/ freeze the stock. Shred the meat from the bones and chop up no fat, skin etc. and use in a chicken chili or bbq sauced shredded chix and wife won't recognize that it's dark meat chicken, just a good chicken flavor. Don't cook in the stock so long that it loses all its flavor to the stock, just cook until done.