Will the insurance company pay for a vehicle that was driven by a suspended license driver that no other cars was involved?

Probably not. Insurance companies will always look for ways to negate or lower the amount of claim damage they have to pay out as compensation.

Driving the vehicle without a license (or a suspended one) would constitute a breech of the contract/ agreement and they would not pay.

Although if the vehicle were stolen and then driven by an unlicensed party (and the incident reported to the authorities), they would have to pay.