Depending on your definition of "internet connected," I'd disagree with your first point. Most new cars come equipped with the hardware for a data-enabled cellular connection and many have been for years. While it's not a feature you necessarily see or know about, it's there. Presumably, the ones that are used by a service like OnStar are constantly polling in the background to get status updates for the account the vehicle is associated with.

But yes, to my knowledge, most (all?) operate fine without a cell signal.