In most cases, yes, the insurance company will pay out on a claim for a stolen vehicle, regardless of whether or not it has a valid MOT certificate. This is because the MOT certificate is not a requirement for the vehicle to be insured. However, some insurance companies may include a condition in their policies that the vehicle must have a valid MOT certificate in order to be covered. In this case, if the vehicle is stolen without a valid MOT certificate, the insurance company may refuse to pay out on the claim.
It is important to check the terms and conditions of your insurance policy carefully to make sure that you understand what is covered and what is not. If you have any questions about whether or not your vehicle will be covered if it is stolen without a valid MOT certificate, you should contact your insurance company directly.