Normally they would, yes. In the same way that your car insurance won't cover you if you are in an accident when driving with tyres considered not roadworthy (if spotted, of course). Equally, some insurance providers (car, pet, whatever) will pay the service provider directly, whereas others expect the policy holder to foot the bill and then reimburse them afterwards.
Insurance providers make it hard to claim for a reason. This is why you read the terms and conditions for things that matter.
Unless you are Broke, of course. Because why bother when you can scrounge off of people?