Awesome! Batches must have begun at some point this morning, so it looks like the FlyerTalk thread is correct, although likely skewed to the 3rd of the month due to the 2nd falling on a Sunday. So, it looks like this is certainly the sequence of events:
a.) Annual fee is billed on the final day of the statement period that your anniversary date falls into.
b.) One full statement must pass after the annual fee has been billed.
c.) The award certificate will appear in your Marriott account on or about the 2nd of the following month.
Example using my own data:
a.) Anniversary date was in March; statement closed 02 April with annual fee.
b.) Next statement closed 02 May.
c.) Award certificate deposited to Marriott account 03 June.
By that logic, had my statement closed on 31 March, just 2 days earlier, it's likely that I would have received my certificate a full 32 days earlier, on 02 May. I don't like rolling statement close dates, though, so all of my Amex accounts are set with due dates of the 27th so that they always close on the 2nd.