self._authenticated is inconsistent for mast

As @ceb8 pointed out in this PR review https://github.com/astropy/astroquery/pull/1874/files#r521553922, there is a bit of room for code cleanup in the mast authentication module.

E.g. I find self._authenticated a bit inconsistent, it's set to `False` only after logout, but not at init when e.g. a token is not provided.

I label this as a bug, but please let me know if you think otherwise.

cc @tomdonaldson @jaymedina

Read the MAST authentication module and compare how self._authenticated is initialized when no token is provided with how it is updated during logout. Confirm the intended unauthenticated state and add or update coverage so the flag is consistent in both paths.

Written by the indexing model from the issue text.