Well, if you can imagine that there is a world where people can use the same device in the same home to access videos (ever heard of families?), surely you can imagine that Google would not terminate all accounts used on that device because they have no clue who is watching what when they are not logged in.
I'm pretty sure they wouldn't care and ban the device
I can imagine it would. My experience tells me it's not out of the question. With Google it's improbable at the moment, but it happened to me (someone got nasty under my ISP's CGNAT) with the other service which will remain unnamed.