You will lose some gp. You cannot run the same gt on 2 boxes at the same time and not lose some gp. If you want to get offline acheivements on your banned console you will have to use the same "active" gt that you use on your other console(not a copy of it but the same actual one) Most people with more than 1 console just keep their gt on a mem card, play whatever games you want on either console, and then when you play on the live enabled one your gs will be updated.
It may be possible to move your gt from your live box to a mem card, put it in your banned console, load savegame that you earned acheivement on, quit game and move mem back to live box. The save should be valid for that gt, but whether it ads gs or not could depend on the game.