Is there a way to have an xbox live login on a permanently off-line xbox, and on an on-line one at the same time?

I've got a brand new xbox that isn't modded that we use for online games as well as Netflix. I'd like to be able to use that one for netflix and at the same time use my modded xbox for offline play. I know I can keep the profile on a memory card and switch it back and forth, but then I can only use one at a time.

If I had two memory cards, and bought the datel card reader to copy the card onto a new one would that work? For example play offline, and every so often swap the cards between xboxs to load my achievements?

Thanks.

It could work but you could get issues with corrupted profile info, in my case i was banned, when i switched to my new untouched xbox my profile was corrupted so i had to delete the gamertag from my xbox and recover it from live.
A friend of mine got his whole GT corrupted by doing this after going to a friends place and recovering his GT there, when he got home and started up his xbox all his acheivments where gone.

once you recover a GT on a non banned, or any live capable 360, the one on the banned system becomes obsolete and outdated.

I had my GT on a card and lost it. I recovered my GT and played for awhile, then months later found the memory card. Just for kicks I plugged it in and it said the profile was not valid. I don't remember the exact message but bottom line, no matter what the GT is on, if you recover it onto something else, it becomes the current GT and as I said, the old one will no longer be usable online.

Your idea would work to use netflix on a clean machine and again on the banned machine. Ever seen "Multiplicity"? when you clone someone, they have all the memories of the original up until the time of the cloning, but after that, they start to become 2 separate identical individuals.

Sorry just to clarify neither is a banned xbox.