MySQL Scheduled Event and server offline?
It should run just fine.

However, it is just like configuring Windows Updates. If you configure Windows Updates for 12:00 AM, shutting down the Windows Machine at 11:59 PM and starting it back at 12:01 AM prevents Windows from checking for Updates.

When such a shutdown is occasional, leaving everything alone will cause the DB server to bring up the MySQL Event at midnight so long as mysqld is running at midnight.