For me, it appeared they acknowledged as soon as they received it, in about a week, which was also the time XpressPost took to deliver it.
The wait from after their acknowledgment to status closed was almost a month.
I checked through my MP's office, explaining I would need time to get a passport for my child. In a few days the MP's office got back to me saying the card has been received, they don't always acknowledge receipt of the PR card (some unconvincing verbiage about why), and that it's all in order and the certificate will be sent in due course.
Unclear of course whether asking the question moved things along but I'm much relieved.