Amex is not going to charge you for insurance on a rental vehicle until you actually have keys to the vehicle at the time you pick it up and have signed the car rental contract.
Be sure to check if the country you are renting the car in requires American drivers by law to have an “International Drivers Permit” or IDP. Spain, Austria, Italy and Slovenia, for example, are just some of the countries that require an IDP. If an IDP is required and you don’t have one, the insurance coverage may be null and void in the event you have an accident— so it’s critical to get one in the countries where it is required.
IDP’s can be obtained for about $30 at any American Automobile Association (AAA) office .