Don't consider this as a definitive answer, as I don't have any standby configuration handy to prove/test my thoughts.

Archivelog mode is written in the controlfile. You can't create standby database file on the primary instance if it is not running in archivelog mode, so initially your standby database will be mounted in archive log mode in any case. You also can't change the mode from archivelog to noarchivelog while your database needs media recovery. In standby database the system assumes the database constantly needs media recovery (you have to specify STANDBY while mounting the database), so I guess it will never allow you to change the mode from archivelog to noarchivelog. So you are bound to archivelog mode with standby database, you can't change that. But even if you could set it to noarchive log I can't see any advatage of running standby in noarchivelog. Neither during recovery nor during database being opened in readonly mode no redologs will be generated, so archiver won't have to do anything and will not use any system resources at all.

Another comment on this statement from one of the previous posts in this thread: "You cannot apply redo logs to any database not in ARCHIVELOG mode". This is simply not true. If you switch your database from archivelog to noarchivelog mode you can still perform a media recovery using archived redologs from the time when the database was in archivelog mode.