I enrolled online on the morning of Monday 16th, through the Amex Plat website, supplying my existing LeClub membership number. I got an email a few minutes ago from Accor welcoming me as a Platinum member, and logging into the website it shows my status as "Le Club Accorhotels Loyalty Platinum"

So, just under 2 weeks for me, guess it depends how quickly you got your application in when yours will turn up... Fingers crossed it's under 4 weeks!