Does this have ical or google cal auto sync features?

It has something similar to sync.

We’ve added option to import .ics events directly from url (for example: https://calendar.google.com/calendar/ical/en.bulgarian%23holiday%40group.v.calendar.google.com/public/basic.ics) every hour or so using the wordpress cron function.

You can give it a try on our live admin demo http://stachethemes.com/wp-demos/tbb/ and see if this works for you.

The feature is located in Dashboard -> Stachethemes Event Calendar -> Import -> Auto-import events from URL