You can keep zucchini noodles raw, or cook them a bit before serving to warm them up and soften them. Either way, I suggest taking this one extra step before serving up yoru spiralized zucchini:
after spiralizing, place the "noodles" into a large strainer or colander, and sprinkle with a bit of kosher salt. Let them sit for 10-15 minutes (you can do this while the no-meatballs cook) and allow them to drain off their excess liquid. Spread on a clean towel and blot gently before piling into bowls (or quickly sauteing in a hot pan, just for a minute or two) and then serving. This will help prevent a watery soup from happening in the bottom of your bowl.
And because I know some of you are going to ask,
this is the spiralizer I use. I've had it for a couple years now, and have been very happy with it so far. It makes quick zoodle dishes and clean up a breeze.