I have the same credit card, and have been told it covers any additional drivers, provided they meet the age and licence requirements, and they do not have to be named on the rental agreement.

It does not have any liability coverage (does it cover damage to persons or property that is not the hire car e.g. another car if you hit it). So you need liability coverage, either in the form of your own car insurance, or liability policy. You would also be wise to ensure anyone else driving the car has such policy as well.