as long as I know, EEPROM doesn't has the data to allow or prohibit backup disk running.
So flashing the EEPROM will not let you run backups.
Is there a way to flash your xbox without soldering, use something to conect the points, hold it for a while, flash the bios, then relese the connection, if you do this you'll see no soldering points, no conductive-pen painting, nothing on the board and your xbox is flashed.