Well... it definitely has time code support of some kind, but I think it is more similar to the S5 (original, and possibly the S5 II / X are similar).
I can't confirm either way about getting timecode though the flash sync port since I didn't get a BNC-to-flash-port adapter :(
However, with firmware 2.1 on my S1, there is no "External Timecode Settings" menu available (while the S1H has that option), so there is no way to set a TC Syncronization, as far as I can tell, through the menu.
I'll try looking in to it a bit more later on. But I think that we just are stuck recording audio timecode to the left channel and then converting to metadata in Resolve. (Suck it, Premiere Pro users!!!)
Unrelated Rant: Wish there was an easy way to store those flash sync port covers when you remove them.