Does the e-mail address that can be specified as the alarm mail sending destination address in the monitoring menu need to be the e-mail address of the user who can access Smart Data Platform Portal?

No. It is not necessary to be the e-mail address of users who can access Smart Data Platform Portal.
An arbitrary mail address can be set as the mail address that can be specified as the alarm mail sending destination address in the monitoring menu.
Reference: Tutorials - Monitoring - Creating Monitoring Alarm