No, but you have to pay for the entire phone up front if you want total reimbursement. Basically, they will reimburse you for the amount you charged on your amex. Say you do installments, but put $300 down. You would get $300 of coverage and it doubles the manufacture warranty. It is only for 90 days on accidental coverage though.
I didn't do a good job of explaining that. There is 90 days of basically applecare+ going through amex in the sense they will cover all types of damage. After 90 days you just have the manufacture warranty for 2 years instead of 1. For example, if you battery died 1.5 years in and apple charge you $200 for a new battery you would be covered assuming you charged at least $200 on a single amex transaction towards the phone.