I found about storj a couple of weeks ago and I've been playing with it¹. I like the idea of shared encrypted storage on the internet very much, specially after watching the Node Summit talk: The cloud is Dead - Long Live the Fog!.
The cloud sucks, but these people are hacking it in a cool way.
Syncthing is better for me than other ugly closed things like dropbox because I have full control over it and I decided that my data must never leave my home network. However, it sounds appealing to keep a backup in the fog, as they call it, for a few of my things. They will never be readable by anyone because the decryption keys will not leave my home network, and it gives me guarantees that I can't have with my small set of relatively co-located devices.
The goal of both projects sounds complementary. And an integration like the one proposed certainly would require work and will possibly encounter unforeseen difficulties, but it makes sense to me.
There are other projects like IPFS, so this work could open the door for some crazy new ideas.
¹ Of course, there's a snap: https://github.com/Storj/storjshare-daemon/blob/master/snap/snapcraft.yaml :D:D:D