Wirelessly posted (Galaxy S2: Mozilla/5.0 (Linux; U; Android 4.0.3; en-us; SGH-T989 Build/IML74K) AppleWebKit/534.30 (KHTML, like Gecko) Version/4.0 Mobile Safari/534.30)
From what i read it is one pull, but to be on safe side do both the apps around same time in two different browsers. This way you do not mess up with when amex clock resets to consider a separate application.
But it us almost sure that 2nd app will not be approved automatically. You need to call them for manual approval.