Settings sync is recently introduced in insiders.
(I don't run insiders, I just saw the announcement in the release notes so this may already be present)
To date I have used an extension for this that operates very well (mega props to the dev): https://github.com/shanalikhan/code-settings-sync

This extension uses private GitHub gists to sync settings, this means that there can be multiple gists for multiple settings "profiles". This is super handy for example where I have settings that I use across machines at work, and different settings that I use across personal machines.

Does, or can, the settings sync feature support similar?

Thanks!