Please Help

Hey I have a question mod related. I am hoping some could help me. I recently acquired a second Xbox 360, it is in need of a few repairs which I plan on doing. I have a new case, a new dvd drive and the Blaster 360 to flash the drive. My first Xbox 360 is unmoded and I play it on Xbox Live. So what I am asking is can I use my harddrive form my first unmoded Xbox 360 in my moded Xbox 360 to recieve the achievements for the games I played on it, and still put it back in my unmoded Xbox and play on Xbox Live?

So the short story is, can I use the same hard drive in two systems, one mod the other not, and if i put it back in the unmod one, will it work fine on Xbox Live and not get me banned? What should I do?

Thank you

 

why are you asking about the 360 in the xbox forums?
There is a 360 area where you might get an answer.