While logged into my Amex CC account, I noticed that I'm "Pre-Approved" for three charge card products:
Since I'm "Pre-Approved," would I incur an inquiry if I applies for one of these cards?
Yes you will still incur an inquiry.
Since you have a Zync already I believe it would be considered a product change which would not require a hard inquiry.
If you apply for a credit card then that would require a hard hit.
My wife has Zync. I have three CCs (Blue Cash, Cash Rebate, HHonors), though I have reasons that I'm interested in potentially getting a charge product.