Now, if I understand correctly, I can go to "Restore Purchases" and it will turn officially into a Max just as if I had maxed it out with purchases, right?

No, that's not correct.  The only way you can officially turn an H9 Core into a Max is by maxing it out through algorithm purchases.  Here are details on the MaxOUT program: https://www.eventideaudio.com/support/downloads/h9-maxout-program

If you have a Max and a Core registered to the same account, you can use the algorithms from the Max on the Core, but the Core remains a Core.