you can use the built in google calendar without any internet connectivity, it just won't sync. you can still use it locally.
Google Calendar, or at least the one I got installed in my first Android phone, required an Exchange account. Without it, it simply didnt continued any step further and was useless. If there is some way to skip that, I didnt found it.
Any.do cal is amazing. I switched over to that permanently when I realized how fluidly it syncs with my Google Account.