Yes. The data of calendars and contacts is stored in the database, so there is no need to install the apps after every upgrade. With version 9.0 the dav-endpoint moved to core and there was a change to the table structure in the database for the data of calendars and contacts. The upgrade script takes care of the data migration. Here is a more detailed article about this: Morris Jobke
What I would do in your case is to backup all calendars and addressbooks. Then upgrade through all the major versions. Or even do a fresh install and reimport the backed up calendars/addressbooks as suggested by @jvillafanez. Depending on the hardware it might be a good idea to import calendars and addressbooks to a client and let the client sync the data to the server. With weak hardware and biggish calendars/addressbooks you might run in a timeout issue when reimporting directly to ownCloud.
If you have access to the server you could use the script calcardbackup to easily backup all calendars and addressbooks of all users.
Good luck!