Unfortunately it's common enough to see this same story in family after family. There are dark-complected people in family, maybe black hair, high cheekbones, that stories developed about possible Native American ancestry. Not only that but it almost always seems to be Cherokee too.
While it could be possible, it's also just as likely to be false. There are German families that fit the description, and then get stereotyped based on the look, and then a myth develops.
If you want to find out, then your best bet would be to take a DNA test. And also put together a well-researched family tree.