Don't. It sounds lucrative and too good to be true because it is a group insurance policy. This means that the policy and cover will apply only as long as you are an Amex customer. If once day they unilaterally decide to close all your cards (which they totally can and will), you will be left holding the bag. It is just the same as your employer health insurance but without any of goodwill and accessibility offered by your employer.
All aspects of the policy is controlled by Amex (and ICICI). You cannot port the policy, make any changes whatsoever to it, and most importantly, are completely left to the whims of Amex when it comes to claims. It also does not build a credit history with the insurer which is absolutely necessary these days.
Spend more and purchase a personal policy from the insurer directly on your terms.