According to this Apple video, it seems possible. The relevant part of the video is here (transcript):
“The next class is the AppConfiguration. And this configuration can be used to display any app. Much of these two classes is the same. So let’s start there. Both classes have a campaign token and a provider token so that you can use SKOverlay with app analytics. They also have functions that allow you to set and get arbitrary key values. Now most developers don’t need to use these but they’re there so you can integrate SKOverlay with other StoreKit APIS such as SKAdNetwork.”
But there are no clear technical information on how to do it (which additionalValue keys to set...)
Unfortunately, I didn't find any additional information.