If I purchase a console banned from Xbox live off Facebook would I be able to have it...

Nope. Console bans are not reversed.

There is no way to check if it is under warranty or not until you purchase it, and then register the console, and buying it from someone on facebook is a risk anyway, as the console could be banned, or broke in some way. You're better off purchasing from
a reputable store, that way you know there is a warranty on the console.

Never buy a used console off Ebay. Odds are it could be tampered with and or banned from Xbox Live. If you buy a used console from Gamestop, they usually come with a one year warranty(check with the retailer first). Though if you are able to purchase a new
console, that route would be your best option honestly.

From Facebook, I searched for the App "Xbox LIVE" and authorized it to have access to my Facebook information. This included a step of logging in to LIVE. After that, I was able to login from the Xbox. I was able to share an achievement, but I had to enter
my FB credentials a second time, and authorize the post. Now when I check my authorized Facebook apps, "Xbox LIVE" appears twice, with different information under each. Anyway, as far as I can tell, there are no instructions stating the FB App authorization
prerequisite. The only clue I found was in the "Remove the connection to Facebook" section of the "Post to Facebook from your Xbox 360 console" topic, which mentions removing the application. Maybe if I had tried to share an achievement first, this might have
worked; I had only tried the Facebook icon on the dashboard.

The PET won't discuss console bans. Sorry, but it's buyer beware when it comes to buying used 360s.



From the console ban FAQ:

Can I still be banned if I purchased a modified console second-hand?

Yes. The warranty on a second hand console is void, and the purchaser assumes the risk for any previous modifications. If you purchase a console that has been previously suspended you will not be able to connect to Xbox LIVE.