Hi @Adam_Ulbricht, welcome to the Asana Community Forum!
You can sync any project, tag, or My Tasks list to an external calendar. This option is currently available for Google, Apple and Outlook Calendar. However, Asana tasks won’t carry over in your Intranet site.
I also suggest you to have a look at this thread with more information about a similar question: How do I make an Asana Calendar viewable to the public? - #3 by Tiara_Moske
I hope this helps!