Adding another Secondary Log Shipping location
Yes, you should apply the latest FULL and all the applicable Transaction log backups in sequence after that full, manually on the secondary with no recovery, prior to setting up the log shipping jobs and turning them on (using the wizard with no initialization).  When the log shipping wizard is used, it will, as you said, create the backup job on the primary and the copy and restore agent jobs on the secondary which looks for the next LSN to apply after the last one you applied manually when it starts applying the logs it needs for the log shipping process to begin.