Im planning to release Game Center connectivity on a future build. Currently my app stores data locally only.
Once I do integrate, will top scores stored be used online?
Anyone? 
You can use unity’s social api for game center or write native code. You will have to submit score to game center whichever path you choose. If you have it stored - then yes, it possible that GC will use your current score, but not without you uploading it to GC.