No, if an insurance company tried to decline a claim because a vehicle wasn’t roadworthy, it would be down to them to provide proof that the vehicle wasn’t roadworthy.
A valid MOT doesn’t guarantee a car is going to be roadworthy for for the following 12 months, it just shows that it was at the time of the test. Consequently, most if not all vehicle insurance policies contain a clause obliging the owner to ensure the vehicle is kept in a roadworthy condition.