>> I tried repotools -archiveuser command and created a batch script to archive multiple users. How safe is this approach on a Production Environment?
It's always best practice to back up your DB prior to running any risky bulk operations. That way, if things go awry you simply restore your backup. Of course, this follows trying things out first in your own local sandbox environment.
An alternative to archiveUser would be to look into the REST API for user management:
https://jazz.net/wiki/bin/view/Main/JFSUsersAPI
https://jazz.net/wiki/bin/view/Main/JFSUsersAPI2

I think this developer works article will benefit you as well: http://www.ibm.com/developerworks/rational/library/automate-management-rational-team-concert-users/automate-management-rational-team-concert-users-pdf.pdf

>> Does repotools take care of the case sensitivities?
Be sure you follow the note in LDAP configuration from the IC:
"If you use LDAP for user management and you enable the option to not use case-sensitive user management, make sure that Jazz Team Server is also configured to allow usermanagement that is not case sensitive. To configure the Jazz Team Server login property, on the Advanced Properties page of the Administrative web interface, modify the  Use caseinsensitive user ID matching  property."

>> What does LDAP sync task do?
http://pic.dhe.ibm.com/infocenter/clmhelp/v4r0/index.jsp?topic=%2Fcom.ibm.jazz.repository.web.admin.doc%2Ftopics%2Fcldapsynctask.html