From http://www.xbox.com/en-US/consoleban/
My console has been suspended. Does that mean my Xbox LIVE account will be suspended as well?
Suspensions for both consoles and accounts are determined by looking at a number of factors. While some Xbox LIVE account suspensions may be issued alongside console suspensions, they are not issued with every single suspension. To avoid having your account suspended from the service, please follow the Xbox LIVE Terms of Use and Code of Conduct
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