Yes you can use the stalks of the watercress plant in soup.
All parts of the watercress plant are entirely edible although the roots of the watercress plant are not that tasty and are best thrown out.
You can use any part of the watercress plant for making watercress soup though or just eat the watercress.
The watercress is chopped up and then added to the soup to make watercress soup.
I always chop up the stalks and every part of the watercress plant except the roots and put them into the watercress soup.
All parts of the watercress contain nutrients, vitamins, minerals and antioxidants so you get more health benefits from the watercress when you eat most of the watercress plant.
Watercress that you buy in the store is edible for all parts of the watercress and the same is true for home grown watercress.