Search mail documents in inbox

Can I use DeliveredDate field to perform the search to search the incoming mail in the inbox?

we cannot use the ‘new mail arrived’ agent in the primary server for performance reasons in our environment. So we have a secondary server to replicate with primary and the agent in the mailbox is scheduled to run on the new in coming mail in the inbox and process them. This is for all the users (about 100 +)

I need a search formula to filter out the new incoming mail. Any help? Thanks.