No, to setup two devices you have to add the id of A into B (you can even scan the qr code), wait for B to be contacted, and from B accept the invitation. Repeat for each folder (there's a setting where you cao automatically accept all folders from a given peer, off by default).
You can also define that one folder on a given device (say a server) never accepts remote changes from anyone else, or never propagates local changes to anyone else. Combine this with encryption (provided by syncthing if you so desire, or your own) and versioning (also provided by syncthing if you want) and you have a pretty good backup endpoint.
I invite you to try out syncthing deeper, the doc really doesn't do it justice. However keep in mind that it's supposed to be used on devices that will be manually deployed. It's not made for large scale deployments.