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[evilgloomy]

if the modded console will not ever go online, there are zero risk of getting banned, they can't check or ban you if you are never connected.  however, you could be banned the moment you connect to live.  

I believe as long as its not banned, you'll still be able to switch profiles between the clean console and the modded console

There are no way to check that the games are backup when syncing the gamertag.  All it looks like is that you were playing your xbox offline.