Hi,
the softmod installs the shadowc to prevent the real c contents from being damaged. If a game tries to update your dashboard, it might cause the softmod to no longer function. When the game only sees the contents of the shadowc, it can alter them without risc for the softmod on the real c.
you still could have issues if you boot the xbox with the game cd in the drive. The xbox will directly boot the game. The softmod and the shadowc aren't active at that moment.
For that reason, the actual C partition is filled until there is no free space left. Due to the lack of free space, an attempt to update the dash on the C will fail.
If you run the M$dash with the softmod operational, it will look for it's files on the shadowc. That's why you should have a copy of the M$dash there.
You could ftp the backup to your pc and burn it to a cd for further use. There is no need to keep it on your xbox harddisk. It is even strongly advised to ftp the eeprom.bin (in the backup) to your pc.
You also need a copy of the M$dash on your real C partition, as that is the one being exploited.
If you really have a lack of space, you should consider installing a larger harddisk in your xbox. That way, you can backup your game disks on the harddisk and run them from there.
regards.