Hello Chris,
Absolutely! Our upgrade process it quite seamless.
Simply install JEvents 3.1.14 via the Joomla! extension Manager, (leave your old one installed, this will replace it).
Then, see:
http://www.jevents.net/updater-access-code
How to get an update code and update the rest via the Joomla! Updater

. All data should be safe and not touched.
However, WE HIGHLY recommend taking a backup before upgrading just in case.
Many thanks
Tony