No. I've known people arrested for that. I'll drive with an expired license, an expired registration but never without insurance. It is just such a stupid thing to do.
The VIN plate is what is insured. The rest of it builds off the insurance. You need insurance on a car to register it. You need a registered, insured car to get a drivers license. The insurance company will pay out, however you will be dropped immediately after and possibly sued.
My understanding is that only one state (North Carolina) requires auto insurance to get a drivers license.
I can offer the anecdote that you can get a drivers license in California by taking the exam in a rented car. Presumably you can borrow a registered, insured car (from a friend, say) in nearly every state?