I'm a Resilio Sync Home Pro user and I also discovered this "feature" last night since I use Resilio Sync iOS app to backup my wife's iPhone "Camera Roll" and she was quite upset when she realized that the wonderful backup I had made didn't contain the "live" stuff. Being an Android guy myself I was aware of "Live Photos" but not that they were made of two separate files (picture + movie). The description given on the Apple App Store is misleading :
*1 : no it doesn't, you must manually open the Resilio Sync application to synchronize once in a while
*2 : unless you are using Live photos in which case your Live part is forever gone.
It's still a wonderful product but please keep improving it.