Yes, you need a level shifter
With a shifter (I used the 96boards-sensors board) I'm able to drive SSD1306 based displays via I2C on DB410C. I even made a video:
Note that the audio mezz is one of the cheapest ways to get a level shifter for 96Boards platforms right now. However be warned that the level shifters on audio mezz board do not tolerate long wires (in the video you will see a long wire between the mezzanine board and the display. Long wires will result in false triggers the edge detection logic in the shifters causing corrupt data (96boards-sensors does not have edge detection in the level shifters; so it cannot clock the bus a fast but does tolerate longer wires). Anyhow, if you use an audio mezz then keep your wires as short as possible!