David, Shihab Hi,
Unfortunately, sync replication and persistent search are different mechanisms, and it appears that OpenLDAP doesn't expose the Persistent Search control. Although, since there are so many ways to configure OpenLDAP, it's possible that we simply haven't managed to set one of our test instances up to correctly expose it.
From a quick review it seems that OpenLDAP does not come with the notion of persistent search, however I found a reference about a possible implementation based on syncrepl, here, Syncrepl client API.
This is not only intended to provide replication capabilities, but also to implement client-side "persistent search"-like feature based on stock slapd (>= 2.3), without the need to revamp the persistent search IDs and code yet another overlay.
Also a pertinent discussion found in http://www.openldap.org/its/index.cgi/Contrib?id=5612;expression=persistent
Prob
Cheers,
A.
Database-backed LDAP caching works for all directory types.