When I saw them in 1983, they were touring with three backing vocalists. I might be wrong about this (it's been a long time and my brain has been through a lot since then), but I believe that when they did Sync I, they rotated through the female singers so they could each take a line and sustain the end note, as Sting does on the album.
In the real three-piece setup, it would be super hard to figure a way to arrange it, as I referenced earlier.
Another thing (man, I am really bumming Dive's high here): while Stewart is triggering a few loops and rhythmic motifs on this tour (very well, I may add), Sync I is purely a synthesizer-driven tune. the whole stacatto burst at the start and most of the interesting stuff in the middle is the sequenced synth.
To play it, Stewart has to stay locked to a click (a metronome in his earpiece, basically), and you have no room for improvisation... and God help you if you get off by a half bar.
So, that's why you probably won't hear Sync I in this live format.
Omegaman, on the other hand, could be done! Could be... if Sting-o wanted to do an Andy tune.
Bird in a flying cage you'll never get to know me well.