No; that doesn't factor into it at all. The home ownership rate is the percentage of occupied houses that are occupied by their owner, rather than being rented. It isn't affected at all by the number of people under each roof.
Which is exactly the point: the home ownership rate does not, contrary to its name, give a real description of what proportion of people own homes. It describes the proportion of homes that are owner-occupied, which is an entirely different thing.
And if what we're trying to do is figure out what the common man (whatever that is) rents or owns, it's a terrible and misleading measure to use.
