We are in the process of switching to a new RAID array and need to copy our MySQL InnoDB database to the new RAID array while minimizing downtime (50GB database). I understand that using rsync on a running MySQL database will not produce a usable copy of the database. However, can I get an exact copy by using rsync on the running database, then completely shutting down mysqld, and running a final rsync? Are there any possibilities of data corruption in this case, if I ensure that mysql is not running with the final rsync is run?
What you are describing should work, however my advice for backing up any database using a filesystem-level backup is that unless the database vendor has approved procedures for doing otherwise you need to quiesce the database before performing a filesystem-level backup (That means "shut the damn thing down").
What you're doing will take advantage of
As with any procedure, before doing this in a production environment you may want to contrive a test case (create a MySQL instance and a DB, back it up, make some changes, shut it down, do your final sync & make sure it works on the cloned box).