how much liquid does it take to cook noodles within a recipe without pre-cooking them

If you are trying to cook pasta this way, I think you'll be disappointed. One of the primary reasons for cooking pasta in oceans of water is to help remove some of the natural starch. When you use minimal water, the starch remains.

Somewhere between 1 and 2 cups water per dry cup noodles.
Varies with how much other liquid is in recipe, wheat used and dryness/age if noodles and how soupy or stew-like you want the finished dish to be (e.g., less with lasagna, more with minestrone).
Make 2 or 3 times and see what ratio you like better.