[Milhouse]

You're right, it is confusing. And Milhouse's answer ("Yes") confuses me too.
Because when you turn on Settings > Advanced > Use local files, it does NOT download anything. It SAYS it is downloading, but it is just taking your locally stored artwork and caching it in Kodi's database.

AD will download and create artwork files if the artwork doesn't already exist locally, otherwise it will use the local artwork file and store the url (local path) in the library (assuming a url doesn't already exist, or if "Overwrite all existing artwork" is enabled).

Of course the filename being written/read is always of the fanart.jpg convention, so if you have multiple movies in a folder and enable "Use local files" there's a risk they will all end up using the same fanart.jpg artwork, particularly if you also enabled "Overwrite all existing artwork", which could be disastrous for your multiple-movies-in-a-folder library.

AD does not touch the texture cache - that is updated only when the new artwork is displayed in the GUI.

Which Kodi actually does fine for itself without Artwork Downloader for poster, fanart, and extrafanart, but seems to require Artwork Downloader when it comes to banner, clearart, clearlogo, etc. At least, that's the way it seems to work for me.

Correct, AD is really of benefit when finding and associating the non-standard artwork types - banner, clearart etc.