Quote: "Quick question: On AppGameKit Player, do the apps behave in exactly the same way as if they were installed from App/Play store, etc.?"
The code (APK or IPA) you upload
is the player (pre-packaged with your game). So yes it should run exactly the same.
However you might have some differences with permissions, IAP, and Ads (since permissions will vary between the AppGameKit Player and your game APK, and IAP/Ads might require your game ID (com.company.game) to be registered and it will only work with that version, meaning you can't test IAP on the Player but you can on the complied APK)