If you are not on probation or parole, you cannot be banned from social media. The U.S. Supreme Court found such laws to be unconstitutional last year. However, if you are a registrant, you will likely still be expected to report that information to law enforcement, usually within 3 business days, and Facebook has it’s own policy to ban registrants from using their site. So you would be able to use it until they find out.
If you decide to try, please get familiar with the reporting requirements in your state and make sure you report it to law enforcement to stay in compliance.