It wouldn't make any difference. While you are required to have at least liability insurance in most US states, I can tell you that here in MN there is no link

It wouldn't make any difference. While you are required to have at least liability insurance in most US states, I can tell you that here in MN there is no link between your insurance status and vehicle registration. When you register a vehicle, they ask for a policy number and expiration date. As long as that date is in the future, the registration will be issued. I know this because there have been times when I couldn't be bothered to look up my insurance policy and just made something up (at work, couldn't log into insurance site for some reason, etc.). Cars registered just fine.