In my experience just recently applying for a Platinum Edge card I found that the sign-up offer applicability was entirely decided by computer. I applied for the card via my Amex login though which was entirely automated, so I dare say the process could be different depending on how you apply (phone, internet, paper form etc).
I had a problem during this application where the previous Amex card I held (and which I supposedly cancelled 2 years prior) was showing up as active in their system, so the computer decided that I was not eligible for the 30,000 MR points sign up bonus. It took a long phone call and an appeal case being raised to the marketing team but eventually I was awarded the points. Anyway, my point is that it’s likely a computer will decide whether you are eligible for the points or not so you will probably be instantly denied the offer if you apply normally.
I would recommend calling them (or emailing) and asking them nicely to waive the last few days off the eligibility based on what a great customer you are going to be for them and if they agree, then doing the application over the phone where you can make sure they will apply the bonus.