I am trying to understand if promoting a read replica to DB instance will maintain the replication/mirroring on the newly create DB instance? Wondering if the newly created DB instance will go out of sync with master.
Yes, it will immediately and permanently be out of sync from the master. Once promoted, you can't undo.
That is the reason you promote a replica -- to disconnect it from the master and make it an independent instance.
The Read Replica, when promoted, stops receiving WAL communications and is no longer a read-only instance.
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_ReadRepl.html