If the owner of a car has insurance, does the insurance cover every other licensed household driver?

Not exactly.  First of all, almost every insurance company, in every state, asks about other drivers in its application form, and if you didn't list them, they aren't covered, at all.  Usually, when you do list other drivers, you either have to provide proof that they have their own insurance, or you have to pay an additional premium.  If you do pay the additional premium, the other drivers will be listed on your insurance.  Of course, this is why people sometimes make the mistake of not reporting the other drivers, to save a few dollars.

You're almost certainly not going to get coverage that you've avoided paying for, if that's the question.