From what I read from the Ableton website, the software cannot directly send SMPTE or Midi timecode, in both case you need to go through "complex" procedures to make it working.
If you succeed to output SMPTE or Midi Timecode from Ableton, non of those protocols can be transmitted via a network cable.
SMPTE needs an audio cable, and MIDI a MIDI cable.
If you absolutely want to send timecode over the network would be to use RTP-Midi on your computer running Ableton.
RTP midi is MIDI over the network, doing this you will be able to connect your computer to the TimeCore via the network, and then use the TimeCore to convert RTP MIDI into SMPTE for your console.