You will not get reinstated. When the first ban wave happened a couple years ago, I called 800 4myxbox and put on a ridiculous hillbilly accent. The idea was to sound so stupid that I wouldn't know what a mod is.
So the first lady I talked to was utterly retarded, telling me that I can't connect to Live because neither of my modems' model numbers were support by XBL. Back then, when you were banned the xbox360 would recommend a connection test, and you'd fail at the end. If you clicked 'more info' it would show you the ban statement.
Then I finally got transferred to another guy after 20 minutes. This guy was looking into the error code I gave him. I hear him typing, but he's not saying anything... then he says "oooooooh". He goes on to summarize that my console was no longer compatible with XBL because some sort of system change has been made. Still using my stupid hillbilly voice, I told him that I "got wun dem fayce-playtes of an American flag, da best darn nation on the planet". About 15 seconds of silence... and he says he'll transfer me to his supervisor who may know more information.
So I get to the supervisor... at this point im over 30 minutes in, still talking like a hillbilly. This lady was smart and was fully aware of the situation. She said your xbox has been modified against terms of use and its banned. She asked where I bought it, I told her from craigslist. She said the person who owned it previously must have done it, but the tools she has available to her do not have any method of unbanning a console. She suggested I go back to the original owner.
This was like 2 years ago. Unless something's changed, they're not reversing any bans.
HOWEVER....
I purchased my console with an extended warranty from the retailer. I told the guy that the online stuff dont work anymore'. I told him I had another one that still works okay when I 'put it on the same plugs' and that I called 'the xbox company' and they told me it wouldn't work again online. The customer service rep at the retailer gave me a new one on the spot. This was right when the iXtreme updated for new XBL compatibility. I bought a new warranty with the replacement console, which ended up getting RRoD. I fixed that by replacing the xclamps for about 3 months, then it died. So I again, returned that one to the retailer for yet another replacement. I bought another warranty. Now I have a new xbox360 just waiting for a new version of ixtreme that is again live safe.