Yes, in fact I use Syncthing myself, and it works ather well. I used to go with Resilio Sync (BT Sync formerly), which is not open source, *and* kept giving me grief, but syncthing has no issues. I share between two laptops, a desktop PC and two smartphones, no problems whatsoever in the past two years or so.

I might write something about my setup later on, it could probably be useful. :)

To be more specific: You can use literally anything that can sync files, since in TagSpaces, everything is saved as files, even meta-data (in a human-readable format, nothing binary), so everything is perfectly portable between systems with any app that can sync files, so Syncthing is a good tool for this.