I did it last year the first night of our arrival. We were staying offsite so I went to Guest Services at Disney Springs. (In the Welcome Center).
They do count the purchase of Memory Maker towards the upgrade, and give you discounts & perks right away.
The only thing you have to wait for is your complementary MagicBand. They have you personalize it and order it on MDE and it’s shipped to your home.
So, just to be clear, you can bridge your tickets to APs before you actually plan to use them on arrival day? Like, we’re arriving on a Monday and our first park day won’t be until Tuesday – can I upgrade on arrival day?
I’m almost positive you can do that, although I don’t have first hand experience with that exact scenario. Maybe @obnurseNH has some insight?
This is exactly what I want to do. My DD arrives 2 days before me and 2 days before our tickets are valid but I am hoping that she will be able to upgrade to an AP on check in . Hopefully @OBNurseNH will have some insight to share. 
Yes. I upgraded to AP upon arrival so as to access the AP discount at dinner that night. We are not parks-on-Arrival-day people.
Thank you. That is helpful.
Thanks!