As far as I know, Orgzly still only works with Dropbox, which is a shame. I wish I had the programming skill to add that support, since Orgzly is open source.

However, Orgzly can sync with local directories on your Android device, so could Syncthing work via that route?

Not sure what you mean by 'out of the box', but orgzly supports local directory syncing which can indeed be used in conjunction. Source: this is my setup.