It depends on what happens with your exact situation, and it's complicated, but here goes:
60% of your FICO score is comprised of the percentage of credit you are using vs. the total limits available to you. This is your Util.% and is the single largest influence on your score.
An Amex credit card affects this percentage normally, by reporting a limit and $0 balance intially, and whatever your balance is after that monthly.
A charge card affects the Util% differently, depending on the options on your account:
If you have a charge card, and do not opt for the extended payment options, then Amex reports the account as "Open / Open Ended" with a 1-month repayment term. This is not a traditional revolving account, and in this scenario the lack of a credit limit will not affect your score negatively. In fact, as the account ages, it will score positively.
However, if you have a charge card with the extended payment features enabled, it is a different story. Amex will report the primary account number as a regular revolving account, but still with a $0 credit limit. While this is technically true, because the card does not have a credit limit (though it does have an unofficial "exposure limit"), this is detrimental to your FICO because the score model then looks to your reported "High Balance" in order to determine the Util%, and that "High Balance" is likely to just be an average month's charges. If you normally charge say $3000 per month, and the highest you've ever charged is $3500, then the lack of a reporting credit limit means that the account always looks "Maxed Out" to the scoring model, as though you were carrying a $3000 balance on a $3500 limit. This will score negatively.
Additionally, if you do utilize the "extended payment", "sign and travel", or "select to revolve" programs, Amex will report TWO accounts when you begin using that option: One for the original charge card account, and a second account for the extended payment balance. The second account's reported credit limit will be the exact amount you initially extended payment on, and so this looks like a second maxed-out account to the FICO scoring model initially (although as you pay it down, it will become positive in scoring). This will score negatively, and remember, this is in addition to reporting the first account as a regular revolving with a $0 limit, which is also detrimental.
But, as the account ages, it will increasingly become a positive factor in your score, regardless of whether you use extended payment or not. A maxed-out 20yr-old account with no lates or derogatory info is still a positive factor, overall. So, just be aware of how it works.
You can also back-door "fix" it by going to best buy or wherever and charging a couple of laptops, and then returning them after Amex has reported your balance to the CRAs. This will ensure that your "High Balance" number is significantly above your average monthly spend, and will help the account look less utilized.