No - your pet does not have to be vaccinated to be eligible for insurance. However most pet insurance policies will not provide cover for a condition which could have been prevented if you could have vaccinated them against it. Without vaccinations, there is also a likelihood that your pet insurance premium will be higher.
Typically, pet insurance providers will not cover the cost of routine vaccinations. You have a duty of care to look after your pet and protect them against potentially fatal illnesses and diseases.