When baking meatballs for a soup, do I have to bake until the meat is fully cooked? I'm making Italian Wedding Soup, and my recipe calls for oven-baking the meatballs for 7-9 minutes before adding them to the soup and boil/simmer for 5 minutes.

Maybe I made the meatballs a bit too big, but it's taking 2-3x the suggested oven time for them to reach 160 degrees (they were only about 110 after the first 8 minutes).

Could I rely on the boil-in-soup step to fully cook the meatballs instead?  Would I have to simmer the soup for more than 5 minutes?  Is this a bad idea?
It doesn't matter in which modality (banking, simmering) you bring the meatballs up to temperature, only that you do.

Normally, if you are cooking them in the oven first, it is for browning generate additional flavor.  Otherwise, you could simply simmer them from the beginning, which is perfectly viable.