ive googled and concensus seems to be it doesnt
The C34J791? Seems like there's little consensus on that topic with many saying it's a panel lottery, though it hasn't stopped one or two review sites loudly declaring it has flawless GSync compatibility. For me it works, though I got the borderless full screen issue on an NVidia card that severely muddied the waters for me. On exclusive full screen it seems to be quite happy between 55 hz and 100 hz - lower and there's the risk of flickering.
On the other hand, I did briefly have another C34J791 that had a physical defect (the bezels were improperly put together and had gaps bleeding light out of them). That screen I returned quickly, but during my brief testing I seemed to have severe problems with GSync, though I wasn't aware at the time of the exclusive vs borderless full screen issue that was affecting my card so can't really draw conclusions about that monitor either (I think I tried both modes, but then sometimes games lie and say they're in exclusive mode when actually they've switched to borderless due to an alt tab or something) - I remember being particularly disappointed in GTA V on that first monitor which was flickering like crazy no matter what I did.
To muddy the waters even more, looks like there's a few versions of this monitor around the world (WTNXZA, WQUXEN and WTUXEN). The UK market seems only to have the latter monitor, while the sites that enthusiastically claim the C34J791 has perfect GSync compatibility seem to be basing that on the oceanic/asian version (one of the other two, can't remember which).
That said, there were circumstances where the second C34J791 seemed to have flawless GSync in exclusive full screen games, like with the Witcher 3, or Forza Horizon 4 (a stealth borderless fullscreen game, but it's a MS one so they seem to have fixed the unacknowledged borderless fullscreen issue affecting GSync for their games only in Windows 10).
TLDR: Hassle free stuff that FreeSync / GSync compatibility lol.
Edit: I suppose another issue that affected things, particularly GTA V, which again confused me as to whether I was seeing flickering or not, was to do with strange gamma shifts, where the screen seemed to dim or brighten slightly depending on the brightness of what scene was on the screen. Did my nut in TBH and may have had nothing to do with FreeSync/GSync, but something else with the monitor.
Life is much simpler now I've downgraded to an RX 550 and am playing Postal 2, with reasonably flawless FreeSync and no anomalies except for the odd loading screen flicker. But then I can't play the games I could on the 1070 Ti anymore, so again difficult to make true like for like comparisons.