Yes, but nobility is something granted by someone in authority. So, the members of the Battle-Born family, for example, are not nobility, and yet may claim to be members of "House Battle-Born". Bryling, however, is a Thane of Solitude (or Hjaalmarch, depending on how you see it), and since that title is only granted by the Jarl, that means she's nobility.
House in this context doesn't only refer to nobility.
I'm not so sure adding "house" to the definition may be a good idea. In this case the word "house" in English is used as a synonym for family or clan and can't be used as such without the appropriate context.
Lol, if House is a synonym for family or clan (regardless of it being a homonym for a dwelling) then it makes perfect sense either for it to be added to the definition of an existing word meaning family or clan, or for a word to be made for it explicitly. Context is the responsibility of whomever uses the word, not the person who makes the language. As you said, this is just my two cents :)