You do not need to submit your application, but you need to create the application in iTunes Connect. Basically, you log all the metadata about your application (e.g. name), but you don’t actually download the binary. In the application management area, you set Game Center ratings and achievements.
Before doing this, you need to create a unique identifier for your application. You create an identifier in the Provisioning area and are called the application identifier there, but when you really select the ID in iTunes Connect, it is called the package identifier.
Please note that the way that iOS actually connects Game Center to your application uses the package identifier in the provisioning profile, so be sure to create a new development profile without wildcards that will be used to create your application.
And finally, it’s important to connect to the test sandbox, and not to the “real” game center during development. Basically, if you are not logged into the Game Center during the game, then a pop-up window will ask if you want to enter the test environment.
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