You would be able to playback a multi-track recording via the SD card playback on the Series III consoles.
In order to do this you would first need to have a multi-track session recorded onto the SD card via the Series III console. Once you have a session recorded you can then press the "Sound Check" button next to the touch screen. Any available recordings will then be available to select via the touchscreen where you can then select the recording you want to use. Once you've selected the desired recording you can select "Load Mix" in the top right corner to recall the mix settings saved from the time of the recording and then press the "Recall" button in the Master Control section.
In order to playback audio from individual channels via the SD card from the Capture recording the channel input will need to be set to "SD Card." Selecting "All Digital Source" on the touch screen will set all channels to the SD Card input source.
This video walks through all aspects of SD card recording and the playback process:
http://support.presonus.com/hc/en-us/articles/115001081306-PreSonus-StudioLive-Series-III-Using-Onboard-SD-Card-Recording