When the connection to the Exchange server is not available you don’t have access to the mailbox.
Starting from Outlook 2010 Microsoft recommends to use Cached Exchange Mode.
When the autodiscover functionality of Exchange is being used you will see that the Cached Exchange Mode will be enabled by default. When using Outlook 2010 by default both the user mailbox and additional mailboxes are added to the cache. It is possible to add Public Folder favorites to the cache but in this case you will need to enable the option manually or via a GPO.
When connected to Exchange messages will arrive with a slight delay in the mailbox.
This is caused by Outlook which will check for new messages every 30 seconds by default.
After that only incremental updates are downloaded from the address book.