Of course, you can sync your calendar with some third party applications, but you're probably looking for a more seamless solution. For that, you need to go through the steps in emusan's Google Market fix:
https://www.mobileread.com/forums/sho...d.php?t=134733. While you can get some gapps to work in some limited ways without it, G-mail and Google Calendar won't automatically sync unless you setup your Google account through the usual process.
I hope this helps. Everything syncs perfectly on my eDGe! :-)