I think it always does the initial connection via the DERP relays, doesn't it? Even if a direct initial connection in theory is possible (no NATs or anything else in the way), the connection itself is always established via the relays, then "upgraded" to a local connection. But maybe they've changed this since I looked at it?

Beyond that, even with a local connection established, all the coordination traffic will still go via the tailnet, those don't suddenly become local-first. But this might also have changed.

What I'm sure is still there today, is that all Tailscale clients automatically upload their logs to Tailscale's servers unless you opt out:

> Each Tailscale agent in your distributed network streams its logs to a central log server (at log.tailscale.com). This includes real-time events for open and close events for every inter-machine connection (TCP or UDP) on your network. - https://tailscale.com/docs/features/logging

Of course, doesn't stop a local connection from working so is only tangentially related, but worth keeping in mind that a "local tailscale connection" still has a lot of external traffic related to it, even though the data you transfer, when possible, uses more local connections.