Will WordPress Auto Update work on a site with Basic Authentication enabled?

Yes, it will work. For Updates, WP reaches out to the update servers, there is no incoming request that is necessary. Your WP doesn’t even have to be publicly reachable at all, you can have it behind a NAT router and (auto-) updates will still work just fine.

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)