Is it possible to take advantage of automatic WordPress core updates but schedule when they occur? I would like to avoid updates happening, say, at 11pm on a Friday, in the event that they cause issues with the site that would require maintenance or intervention.
Core updates (as other things that happen without explicit action by admin) are scheduled. However WP scheduling system (WP Cron) act on intervals (every N seconds) and has certain amount of drift on top since it it triggered by visits to the site.
In a nutshell it's not too favorable to implement more elaborate date/time rulesets into it firing.
You could reverse the logic by preventing core updates within certain times, but really I would recommend to stick with security-only auto updates or manual updates altogether if your site is sensitive enough to it.