To my knowing:
Microsoft doesn't check the contents of your harddisk.
Microsoft checks the bios in use on your xbox. If the bios isn't an original microsoft one, the xbox will be banned.
So, if you try to access live with a mod enabled, the xbox is banned. For that reason, some softmods disable live when they are active.
Microsoft pairs your harddisk and your mobo when you go on live the first time. This means that you can't change the harddisk of an xbox that went to live. If you go on live with the new harddisk, the xbox will be banned.
For that reason, people sell eeprom.bin files of xboxes that never went on live before. Writing such a file to your xbox eeprom is like giving your console a new identity. There are 3 different eeprom formats that are not interchangable. You have the 1.0 version, the 1.1 to 1.5 version and the 1.6 and 1.6b version.