Hi lawday, welcome to our forum.
If I understand correctly (what you're writing isn't very clear to me) you want to use backupped games (it isn't allow to copy games you don't own, only those you do own!) on an XBOX, while not loosing the rights to use XBOX live.
Well this can be done, but I don't exactly know how. The only way I know it can be done, is making use of a mod-plug. This plug is insterted into the XBOX frontally (I guess it's using USB) and can be unplugged anytime, reverting your XBOX back to the original state.
Maybe there are modchips outthere that have some kind of stealth mode, making it possible to hide themselves for the live part of the XBOX... but I'm not sure about that!