Canon 5D Mark III SMPTE Time Code
The info that I have read suggests that there is a way of embedding TC into the 5D3, but no indication of how it is done.
The 5D3 had a stereo audio track, so one track could be used for the TC and the other with mono audio from the audio mixer that feeds the external TCed audio recorders/devices. If the video/audio can be time stamped with the incoming TC then Premiere should be able to snap the video to the time line as well as the audio.
Any imported audio that is similarly time stamped will also snap to the correct part of the time line. Does the 5D3 have a separate TC input or perhaps there is a menu item that makes the 5D3 look at say the left audio channel which has the TC and then time stamps the video? The system will still be free running, unless the 5D3 internal clock can be synched to the incoming TC. In the professional video world this is common practice.