Generally, old media don't die. They just have to grow old gracefully. Guess what, we still have stone masons. They haven't been the primary purveyors of the written word for a while now of course, but they still have a role because you wouldn't want a TV screen on your headstone. (Douglas Adams)
The default synchronization works as follows:
Inbox — whole messages are synchronized.
Other email folders — only message headers and body in plain text are synchronized.
Events — whole events are synchronized.
Contacts — whole contacts are synchronized.
Tasks — whole tasks are synchronized.
Notes — whole notes are synchronized.
Upon each startup of Microsoft Outlook, Kerio Outlook Connector synchronizes the currently opened folder first.
This can be changed; the link explains how. Don't neglect the "Set also to all subfolders".
Of course this does require additional local storage. You might also want to know the cached data is not encrypted.