I've heard of insurance contesting a claim because the pilot had an accident while practicing cross wind landings. If he needed to practice them, they claimed, then he was not capable of landing in a cross wind and should not have been attempting them!
The light sport pilot license is so new, almost every question about what an insurance company might do is hypothetical. There has not been enough actual cases on which to base anything.
I think the best thing to do would be to base the question on an automobile accident.
Suppose a pilot is diagnosed with high blood pressure and takes medication to lower the blood pressure. His doctor tells him there are no side effects that would prevent him from driving a car.
The pilot is diving to the airport when he has an accident. Would the insurance company be apt to deny a claim if it were demonstrated that the driver had a medical condition that had been diagnosed well before the auto accident, a condition that might or might not have contributed to the accident? Would this result in an endless round of litigation?
That is a possibility, isn't it? So anything that can be hypothesized about a car accident could also be hypothesized about an accident of a light sport pilot in a light sport plane.
So, exercise prudence and fly the plane.