We use a git+composer strategy to manage our WordPress environments (start here for a series of posts about this) and therefore have WordPress auto-update disabled. Beyond that, Apache doesn’t have write to its own filesystem, so WordPress can’t update itself.
However, the update and upgrade buttons are still presented on the interface, and it’s possible to accidentally trigger the update process from there. When that happens, WordPress places itself in maintenance mode, tries to update itself, fails, and then takes itself back out of maintenance mode. It’s about 5-10 minutes of downtime depending on your caching strategy.
WordPress also leaves behind a memento in the form of a message displayed to every administrator (both network and site on multsite environments), informing them that “An automated WordPress update has failed to complete.” This message is easy to remove, but you may have to take multiple actions to do so.