If your insurance company denies a claim can the state revoke your driver license just as if you were carrying NO insurance?

Yes, If you are in an At Fault accident for which your state law requires you carry the appropriate coverage and the insurance you bought does not cover it. Then you were in fact uninsured for that accident and you are not in compliance with your state law regarding your financial responsibility.

Basically it means that you did not have the minimum coverage required by your state.