No idea. I do remember a thread a while back, three or four months maybe, where someone said they received an offer for a secured Amex. They had to back it with a $10K CD if I remember correctly. Can't remember if they applied for a card and got that as a counteroffer or if they just received the offer in the mail. I also don't remember what their issue was as to why they couldn't get an unsecured Amex, i.e., I don't remember if they had a BK on their report.
You can probably find the thread by searching for Amex, secured, CD, something along those lines. You could also call and ask Amex if that is an option. Not sure it is worth it to tie the money up in the CD especially given how horrible CD rates are right now, but that is a decision for you.
Starting Score: ~500 (12/01/2008)Thank you, Walt. I remember that thread. They'd been turned down for regular AMEX but because, I believe, they had a corporate account, they were offered secured or something.
I'm going to open an account with them anyway. And I figured it was a long-shot... more like a javelin throw that it might be considered, but it can't hurt. I need to have my money spread around anyway and AMEX is just as good as anywhere else... well, I thought that with Lehman but that is another story! 
You might also try searching for a group of threads on the Amex True Earnings/Costco card from earlier this year. There were several reports of members obtaining this card with a BK reporting. I'm no expert on Amex, but it seems that they may have changed their tune a bit, over the last year, and that they may not be rigidly BK unfriendly as they used to be, at least not with this product. I recall speculating, when people first started reporting obtaining the card with ta BK, that the housing bust & the economy overall probably shook them up a bit, and made them realize that things aren't always black and white.
Besides, I think that the Amex True Earnings card is their best product-- although, I may change my tune on that if Blue Cash Preferred turns out to be a profitable as I think it'll be! 
That is an interesting question about the Amex Savings account and whether it can help influence Amex's opinion of someone in the "relationship banking" sense.
I know when I sit down at Chase, they can see EVERYTHING I have with them on their screen. Checking, savings, credit cards, CD's, etc. I believe Citi is the same way.
Why would Amex, one of the more sophisticated financial services firms out there, be any different?
I put 5 figures in one an Amex savings acounts a couple weeks ago simply because they are paying a very decent interest rate for savings (1.15%) compared to most everyone else these days.
And, like the OP, figured it couldn't hurt build my spendability with them and chances for a Amex revolver. (Was approved for one today actually).
And then I listed it as one of my "pay from" accounts for my PR Gold card, so it has visibility to the CC people, along with my other checking accounts I pay my CC bill with.
I also believe they can see what you have in those linked accounts (based on something an Amex collections guy said to me 25 years ago when I was a young, irresponsible credit neophyte).
But who knows?
That is accurate, they are 2 different entities, but owned by the same parent however.
Most commercial banks have separate card units handling their card business, but the all co-market each other's products.