You cannot turn on transaction logging for databases on the primary database server while you are using HDR. You can turn logging off for a database; however, subsequent changes to that database are not duplicated on the secondary database server.
After you turn on logging for a database, if you start data replication without performing the level-0 backup on the primary database server and restore on the secondary database server, the database on the primary and secondary database servers might have different data. This situation could cause data-replication problems.