It’s fine. If you recover it to another HDD and console.
On your CURRENT console, it’ll continue to work, but it won’t upload to Live and is therefore meaningless. If you put your HDD onto another console, everything gets corrupt.
SO, if you get another system…you’ll have to start from 0% on EVERY achievement and every game. MS really F’ed us with that one. I understand them being mad about Live, but they have no right to take away my HDD access even if I did modify my box. What if I play games I legally own but don’t want to scratch the disc? How do they know I’m actually downloading them?