Do US auto insurers penalize uninsured motorists?

I'm turning 25 at the end of August, and my insurer has told me they are canceling my current policy on 8/27 if I do not pay today. That's fine with me, because my premium is so high right now due to 4 at-fault accidents on my record (& the fact that I live in an expensive-insurance zip code). Two of those accidents come off my record starting in September, and due to that and my age change I'm thinking my insurance would come down $800-$1000 less than the premium I'm paying now for 6 months (over $2000). The penalties accrued in my state amount to $175 for re-registration of an uninsured vehicle, and I figure if I go to the DMV right away with my new insurance card, explaining that I did not drive my car between 8/27 and 9/1 (or whenever my new policy starts), I can get away without any additional court fees or tickets on my record. But I'm wondering what the insurers will think if I try to sign up for insurance without any preexisting. Do they penalize (with rate hikes) for this?