Well, mostly. However, on a multi-lane highway, where overtaking on the inside is not allowed (here in Europe), Autopilot will refuse to move forward if it means performing an illegal manoeuvre so it isn't quite as driving-side agnostic as you suggest. Also, when using 'Navigate on Autopilot', would it miss an exit because it thinks it's in the wrong lane?
I'm just curious if anyone knows what happens in these cases (and in others that I haven't thought of...)