I would think that you're probably fine to apply for a zync now. However make sure this is the card that you really want. I received my zync in november and have quickly realized why the annual fee is low. The rewards are CLEARLY not the same. Most people are saying that its a good way to "get in" with amex. I agree if you are borderline, however, why not wait a little longer and apply for at least a green. I realized I made a mistake and applied for a gold a couple days ago. I was denied because my time with amex is too short, they also stated that I dont have enough available credit in comparison to my limits, which is garbage. I owe 162/ 8k.. My ex score was 733. Im not saying that this isnt a good card. Just be very aware of the product you are getting. Because if you are approved for a zync and like me find it isnt what you really want but were blinded by the appeal of any amex, you may be stuck with are card you wont use... but it does look pretty.
Starting Score: 617 EQ 10-17-11