I haven't looked into any automation options, but I doubt it. Seems like Working Copy takes a specified folder in the "Files" app and treats it as a git repo (in this case, the Obsidian/YourVaultHere folder). When you launch Working Copy you're basically sitting at a (very nice) git UI, so all the standard git workflows are present.

I'm used to using a variety of editing software and then manually pushing my notes repo, so the lack of automatic syncing doesn't bother me. In fact, I prefer it. I've been burned by auto-syncing before and it makes me nervous.