In my experience having an Amex Savings account does not increase your chance of approval for a credit or charge card.
I was approved for a BCE with a marginal EX FICO score of 649 and given only $500 limit and their version of "credit steps." I subsequently applied for both the Green & PRG cards and was denied despite having over $20K in my Amex Personal Savings account. It wasn't until my EX score got above 680 that I started seeing pre-approvals for the PRG and was approved when my EX score was 698.
The question has been asked before and the consensus is that having a Savings account does not help: See http://ficoforums.myfico.com/t5/Credit-Cards/amex-savings/td-p/1119826
Also, the disclosure statements from American Express FSB (which manages the savings account) specifically state that they don't share information on a customer's creditworthiness with other Amex affiliates: https://personalsavings.americanexpress.com/glbanotice.html
