Didn't use Amex savings to obtain an invite, but as an existing cent cardholder who also once had a sizable deposit via Amex savings I can tell you that they don't factor it into other things as you might imagine would make sense to.

Also, their rates haven't been compatible for the past few years. They used to be in the general ballpark as what Vanguard and others offer via money market funds, but once rates became elevated Amex was slow to raise their rates, and once they did they have never reached the neighborhood of prevailing "good" rates.

I would not consider placing a large deposit into Amex savings as a way to obtain an invite, but if their rates and terms are what you want then by all means it certainly doesn't hurt your chances in any way.