That’s how we do it. Even on hot dogs (beef franks). Sear the franks till browned, remove, add the sauerkraut till browned not dried. I add caraway seeds if the kraut didn’t have any (before cooking). Put the franks back in the skillet, cover with lid for just a few more minutes.
You are the first person ever to know about cooking kraut that way. Although I’m a NO on the caraway. Even brought a dish to a kraut potluck at our parish years ago. There were about 15-20 different dishes mine was the only one like this. And people said they had never heard of it before. My Dad always made it this was with pork, although with stuffed cabbage and short ribs it was the wet pot method.