Beaglebone Black LCD/TFT/display and I2C2
Ask 4D, or the 4D forum.  

However, it looks to me that the I2C bus is used only for an on-board EEProm interface.  Probably to store/read setup and user data.  I would guess that there's plenty of bandwidth left over on the bus for you to use.  

Do be aware that this board has the pull-ups already installed for this bus, so be careful about adding more pull-ups elsewhere.  See the "ID EEPROM" section of the schematic in the datasheet, Page 8.