Yes, you do. And in order to boot that, your HDD needs to be locked.
Then play all the xbox live you want.
NOTE:
DO NOT upgrade your HDD w/o replacing your eeprom or you'll get banned.
Also, don't even think about running live from a hacked BIOS (IE, A BIOS that's not retail kernel/ an official M$ BIOS) or you'll get banned as well.
Happy gaming!