Usually it's best to cook dried noodles in boiling water, and drain and rinse them in cold water when they are done. This does a couple of things:
- helps ensure that the noodle is equally cooked all the way through (instead of getting overcooked on the outside by the time the centre is cooked).
- by using separate water, you don't fill your broth with starch, which would adversely affect the taste, colour and consistency.
If you want to add the noodles directly to the broth, I would recommend rinsing them in cold water first (like you would with rice) until the water runs clear. This will prevent excess starch from being added to your dish.
You could also try adding a stock cube to the water that you boil the noodles in, if your goal is simply to make the noodles more flavourful.