no.
the golden rule prescribes a positive action - to actively treat others in a specific way. the nap is a statement of negative liberty, that tells you what not to do to avoid infringing on the rights of others.
courts have routinely rejected the good samaritan principle, and most libertarians would reject the idea that you have any necessary prerogative to go out of your way to treat others as you want to be treated. i might even argue that it's part of the point of being a libertarian.
but, if we're to eliminate the state, we have to replace it with self-policing and the nap plays a vital role there in ensuring that we have a good heuristic to understanding what we should and should not do.