Hi socialfluency,
Any upgrade could possibly break a custom template, it all depends on how it was built. Given that you have a “troubled” site, plus you’d be upgrading from Events Calendar PRO 2.x to 3.x (a major upgrade), I would recommend that you make a backup, possibly duplicate the site, manually install the plugin, and see what happens. If it all goes wrong, you should be able to restore from backup, or just scrap the duplicate site while you plan your next move.
If you have any other questions specific to the calendar, please let us know.
— Julie