I'm not an expert, but based on my experience with them, I am going to say no.
I applied for the HH Ascend card on 3/13 and was denied w/ a FICO of 643.
I just applied today for it again because I had a pre-approval and since my score had gone up to 670 (due to erroneous late payments being removed from my CR) and was approved. So within a month after a denial, I was preapproved. I think as long as you don't burn AMEX, you should be ok to apply if you see a pre-approval. I think, though some people DO get denied, most of the time pre-approvals are solid.