I know there are a couple IndyCar tubs that are insured; with that said, I'm sure you could insure your sprint car. Heck, you can insure just about anything if you're willing to pay the premium. However, I'd imagine those premiums would be sky-high and not cost effective- you'd be better off putting those premium payments towards a second car.
Somewhat O.T. but you can buy $1500-deductable crash damage insurance for Cory Kruseman's Sprint Car School for $50.00 but it's not available for the race rentals; he told me something along the lines of "When you're racing, the insurance company automatically assumes the accident was your fault"...
Chizmark-
Larsen Agency in Joliet, Illinois came to one of our meetings several years ago and offered insurance coverage but I think it did not include the race car when the race car was on the track.